2d:null 2e:["$","title",null,{"children":"호기심 해결 in 주식시장: VIX 계산편 | Humble Data Miner | Observable"}] 33:Tda8,--- ## VIX 계산과정 서술 (기준일: ${dates[0].toISOString().split("T")[0]}) 1. 사전 파라메터 설정 * N₁(Near-term): (기준일+30일-7일)이후 최근 만기날짜, N₁=${dates[1].toISOString().split("T")[0]} * N₂(Next-term): (기준일+30일)이후 최근 만기날짜, N₂=${dates[2].toISOString().split("T")[0]} * T: 1년대비 만기까지의 시간, T₁=${data.near.T.toFixed(4)} T₂=${data.next.T.toFixed(4)} * R(무위험이자율): 미국국채이율을 기간 T에 맞춰 사용 * 설명의 단순함을 위해 1개월이율 R=R₁=R₂로 간주, R=${R.toFixed(4)} * E^RT: T기간동안의 무위험이익배율, E^RT₁=${data.near.Ert.toFixed(4)} E^RT₂=${data.next.Ert.toFixed(4)} * 설명의 단순함을 위해 E^RT₁=E^RT₂≈1.0로 간주 1. 호가 데이터 수집 * N₁,N₂를 만기로하는 SPX옵션들의 호가정보 수집 (장마감후 수집 권장) * 출처: [Cboe - SPX delayed quotes](https://www.cboe.com/delayed_quotes/spx/quote_table) 또는 [Yahoo finance - ^SPX options](https://finance.yahoo.com/quote/%5ESPX/options?p=%5ESPX) 1. 만기일 기준가 설정 * 임시기준옵션: 같은 Strike상의 PUT,CALL간 호가차이가 가장 적은 옵션 * F: 임시기준옵션의 bid,ask로 산출한 이론상 기준가, F₁=${data.near.F.toFixed(0)} F₂=${data.next.F.toFixed(0)} * K₀: F ≥ Strike를 만족하는 가장 큰 Strike값, K_0,1=${data.near.K0.toFixed(0)} K_0,2=${data.next.K0.toFixed(0)} 1. 불필요한 PUT/CALL 옵션 삭제 * In-The-Money(당장 행사가치가 있는) 옵션들 * bid가 0인 항목과 두번연속 bid 0으로 나온 이후의 모든 변두리 옵션들 * (선택적) 만기일에 SPX,SPXW가 혼재시 SPX옵션만 사용 * SPX옵션은 만기일 오전, SPXW옵션은 만기전일 오후 마감 1. 선별된 개별옵션 K_i에 대해 추가 계산 * Q(K_i): bid와 ask의 평균, ${tex`Q(K_i)=(bid_i+ask_i)/2`} * C(K_i): 변동성 기여분 계산, ${tex`C(K_i)=\frac{\Delta k}{K_i}e^{RT}Q\left(K_i\right)`} 1. N1,N2 각각의 σ²과 최종 VIX계산 * ${tex`\sigma^2=\frac{2}{T}\sum_{i}\frac{\Delta k}{K_i}e^{RT}Q\left(K_i\right) - \frac{1}{T}\left[\frac{F}{K_0}-1\right]^2`}, σ₁²=${data.near.V.toFixed(5)} σ₂²=${data.next.V.toFixed(5)} * ${tex`VIX=100\sqrt{interpolate(\sigma_1^2,\sigma_2^2,30days)}`}, VIX=${data.VIX.toFixed(2)} * 기간별 ${tex`VIX_1=100\sqrt{\sigma_1^2}`}, ${tex`VIX_2=100\sqrt{\sigma_2^2}`}, VIX₁=${data.near.VIX.toFixed(2)} VIX₂=${data.next.VIX.toFixed(2)} 34:T2112,{ const [N1,N2] = [data.near, data.next]; const [e1,e2] = [d3.extent(N1.sel,e=>e.st),d3.extent(N2.sel,e=>e.st)]; const [wf,wl] = [Math.max(N1.sel[0].dk,N2.sel[0].dk), Math.max(N1.sel[N1.sel.length-1].dk,N2.sel[N2.sel.length-1].dk)]; const pmax = Math.max(d3.max(N1.sel,e=>e.mid),d3.max(N2.sel,e=>e.mid)); const cmax = Math.max(d3.max(N1.sel,e=>e.cont),d3.max(N2.sel,e=>e.cont)); const [D0,D1,D2,DE] = [new Date(currdate*1000),new Date(near_quotes.date*1000), new Date(next_quotes.date*1000),new Date((currdate+30*24*60*60)*1000)]; const ex = [D0, D2]; const dates = [D0,D1,D2]; const ey = [Math.min(e1[0],e2[0])-wf/2, Math.max(e1[1],e2[1])+wl/2]; const height = (ey[1]-ey[0])/2; const center = width/2*30/27; const note_unit_height = 20; const note_height = note_unit_height*4; const margin = {top:20,left:40,right:40,bottom:20+note_height}; const svg = d3.create("svg").attr("width", width).attr("height",height); svg.append("rect").attr("width",width).attr("height",height).attr("fill","none").attr("stroke","lightgrey"); const x = d3.scaleTime().domain(ex).range([margin.left, center]); const y = d3.scaleLinear().domain(ey).range([margin.top, height-margin.bottom]); const half_plot_width = x(D1)-x(D0); svg.append("g") .attr("transform",`translate(0,${height-margin.bottom})`) .call(d3.axisBottom(x).tickValues(dates).tickFormat(d=>d.toISOString().split("T")[0])); svg.append("g") .attr("transform",`translate(${x(D1)},0)`).call(d3.axisRight(y)); svg.append("g") .attr("transform",`translate(${x(D2)},0)`).call(d3.axisLeft(y)); const ps = (p)=>p*half_plot_width/pmax*4/5; // price-scale-adjustment const cs = (c)=>c*half_plot_width/cmax; // contribution-scale-adjustment const [NS1,NS2] = [N1.sel,N2.sel]; const up_y = (ds,i)=>i==0?ds[i].st:(ds[i-1].st+ds[i].st)/2; const dw_y = (ds,i)=>i==(ds.length-1)?ds[i].st:(ds[i+1].st+ds[i].st)/2; const cont_color = d3.schemeCategory10[2]; const to_cont_calc_str = d => `${d.label}(${d.st})의 변동성기여분 (${d.dk}*${d.mid.toFixed(2)})/${d.st}^2≈${d.cont.toFixed(7)}`; const to_opt_quote_str = (d,ed) => `${ed.toISOString().split("T")[0]}만기 ${d.label}(${d.st})옵션 Strike가격(k):${d.st} bid/ask중간값(Q):${d.mid.toFixed(2)} 인접옵션간너비(Δk):${d.dk}`; const y_note = height-note_height; svg.append("path").attr("d",`M ${margin.left} ${height-note_height} v ${note_unit_height*2}`).attr("stroke","black").attr("stroke-width",1); svg.append("path").attr("d",`M ${x(D1)} ${y_note} v ${note_unit_height*2}`) .attr("marker-end","url(#arrow)").attr("stroke","black").attr("stroke-width",1); svg.append("path").attr("d",`M ${x(D2)} ${y_note} v ${note_unit_height*2}`) .attr("marker-end","url(#arrow)").attr("stroke","black").attr("stroke-width",1); svg.append("path").attr("d",`M ${x(D0)} ${y_note+note_unit_height/2} H ${x(D1)}`) .attr("marker-start","url(#arrow)").attr("marker-end","url(#arrow)") .attr("stroke","black").attr("stroke-width",1).attr("stroke-dasharray","2 2"); svg.append("path").attr("d",`M ${x(D0)} ${y_note+note_unit_height*3/2} H ${x(D2)}`) .attr("marker-start","url(#arrow)").attr("marker-end","url(#arrow)") .attr("stroke","black").attr("stroke-width",1).attr("stroke-dasharray","2 2"); svg.append("text").attr("x",(x(D0)+x(D1))/2).attr("y",y_note+note_unit_height/2).attr("dy",-2) .attr("font-size","smaller").attr("font-weight","bold").attr("text-anchor","middle") .text(`T1=${(D1-D0)/(60*60*24*1000)}일/365일=${N1.T.toFixed(4)}`); svg.append("text").attr("x",(x(D0)+x(D2))/2).attr("y",y_note+note_unit_height*3/2).attr("dy",-2) .attr("font-size","smaller").attr("font-weight","bold").attr("text-anchor","middle") .text(`T2=${(D2-D0)/(60*60*24*1000)}일/365일=${N2.T.toFixed(4)}`); svg.append("text").attr("x",x(D1)).attr("y",y_note+note_unit_height*2).attr("dy",2).attr("dx",20-2) .attr("font-size","smaller").attr("font-weight","bold").attr("text-anchor","end").attr("dominant-baseline","hanging") .text(`VIX1(${(D1-D0)/(60*60*24*1000)}일)=${N1.VIX.toFixed(2)}`); svg.append("text").attr("x",x(D2)).attr("y",y_note+note_unit_height*2).attr("dy",2).attr("dx",-20+2) .attr("font-size","smaller").attr("font-weight","bold").attr("text-anchor","start").attr("dominant-baseline","hanging") .text(`VIX2(${(D2-D0)/(60*60*24*1000)}일)=${N2.VIX.toFixed(2)}`); svg.append("path").attr("d",`M ${x(D1)+20} ${y_note+note_unit_height*5/2} H ${x(D2)-20} M ${(x(D1)+x(D2))/2} ${y_note+note_unit_height*5/2} v ${note_unit_height/2}`) .attr("marker-end","url(#arrow)").attr("stroke","black").attr("stroke-width",1); svg.append("text").attr("x",(x(D1)+x(D2))/2).attr("y",y_note+note_unit_height*3).attr("dy",2) .attr("font-size","smaller").attr("font-weight","bold").attr("text-anchor","middle").attr("dominant-baseline","hanging") .text(`최종VIX(${(DE-D0)/(60*60*24*1000)}일)=${data.VIX.toFixed(2)}`); svg.append("text").attr("x",(x(D1)+x(D2))/2).attr("y",y_note+note_unit_height*2).attr("dy",-2) .attr("font-size","smaller").attr("text-anchor","middle").attr("dominant-baseline","hanging") .text("interpolation"); // params: DataSet(Near-term,Next-term selection), Expire Date, draw direction(left:-1,right:+1) function draw_quote_spread(Meta,DS,ED,dir) { svg.append("g").selectAll("path") .data(DS) .join("path") .attr("d",(d,i)=>`M ${x(ED)} ${y(up_y(DS,i))} h ${dir*ps(d.mid)} V ${y(dw_y(DS,i))} h ${-dir*ps(d.mid)}`) .attr("stroke","white").attr("stroke-opacity",0.3).attr("fill",d=>d.color) .call(node=>node.append("title").text((d,i)=>to_opt_quote_str(d,ED))); svg.append("g").selectAll("path") .data(DS) .join("path") .attr("d",d=>`M ${x(ED)} ${y(d.st)} h ${dir*cs(d.cont)}`).attr("stroke",cont_color); svg.append("g").selectAll("circle") .data(DS) .join("circle") .attr("cx",d=>x(ED)+dir*cs(d.cont)).attr("cy",(d,i)=>y(d.st)).attr("r",3) .attr("stroke","white").attr("fill",cont_color); svg.append("g").selectAll("text") .data(DS) .join("text") .attr("text-anchor",dir>0?"start":"end").attr("dominant-baseline","middle").attr("font-size","small") .attr("x",d=>x(ED)+dir*cs(d.cont)).attr("y",(d,i)=>y(d.st)).attr("dx",dir*2) .text(d=>d.cont.toExponential(1)) .call(node=>node.append("title").text((d,i)=>to_cont_calc_str(d))); svg.append("g").append("text") .attr("text-anchor",dir>0?"end":"start").attr("dominant-baseline","auto").attr("font-size","small").attr("font-weight","bold") .attr("x",x(ED)).attr("y",y(Meta.F)).attr("dx",-dir*2).attr("dy",-2) .attr("fill",d3.schemeCategory10[4]) .text(dir>0?`${Meta.F.toFixed(0)}=F2`:`F1=${Meta.F.toFixed(0)}`); svg.append("g").append("text") .attr("text-anchor",dir>0?"end":"start").attr("dominant-baseline","hanging").attr("font-size","small").attr("font-weight","bold") .attr("x",x(ED)).attr("y",y(Meta.F)).attr("dx",-dir*2).attr("dy",2) .attr("fill",d3.schemeCategory10[4]) .text(dir>0?`${Meta.K0.toFixed(0)}=K0,2`:`K0,1=${Meta.K0.toFixed(0)}`); } draw_quote_spread(N1,NS1,D1,-1); draw_quote_spread(N2,NS2,D2,+1); return html` ${svg.node()}

${tex.block`\sigma_1^2=\frac{2}{T_1}\sum_{i}\frac{\Delta k}{K_i}e^{RT_1}Q\left(K_i\right) - \frac{1}{T_1}\left[\frac{F_1}{K_{0,1}}-1\right]^2`} ${tex.block`\sigma_1^2=\frac{2}{${N1.T.toFixed(4)}}${N1.SC.toFixed(6)} - \frac{1}{${N1.T.toFixed(4)}}\left[\frac{${N1.F.toFixed(0)}}{${N1.K0.toFixed(0)}}-1\right]^2=${N1.V.toFixed(5)}`} ${tex.block`VIX_1=100\sqrt{\sigma_1^2}=${N1.VIX.toFixed(2)}`}

${tex.block`VIX=${data.VIX.toFixed(2)}`}

${tex.block`\sigma_2^2=\frac{2}{T_2}\sum_{i}\frac{\Delta k}{K_i}e^{RT_2}Q\left(K_i\right) - \frac{1}{T_2}\left[\frac{F_2}{K_{0,2}}-1\right]^2`} ${tex.block`\sigma_2^2=\frac{2}{${N2.T.toFixed(4)}}${N2.SC.toFixed(6)} - \frac{1}{${N2.T.toFixed(4)}}\left[\frac{${N2.F.toFixed(0)}}{${N2.K0.toFixed(0)}}-1\right]^2=${N2.V.toFixed(5)}`} ${tex.block`VIX_2=100\sqrt{\sigma_2^2}=${N2.VIX.toFixed(2)}`}

`; //return svg.node(); }35:Ta41,data = { svg_defs_arrow; function transform_quote_data(raw_data,T) { const merged = raw_data.strikes.reduce((acc,cur)=>{ acc[cur]={st:cur}; return acc; },{}); raw_data.options[0].puts.forEach((put,i)=>{ Object.assign(merged[put.strike],{ pb:put.bid,pa:put.ask,pp:(put.bid+put.ask)/2 }); }); raw_data.options[0].calls.forEach((call,i)=>{ Object.assign(merged[call.strike],{ cb:call.bid,ca:call.ask,cp:(call.bid+call.ask)/2 }); }); const merged_list = Object.values(merged); merged_list.forEach((e,i)=>{ if(e.hasOwnProperty("pp") && e.hasOwnProperty("cp")) { Object.assign(e,{diff:Math.abs(e.pp-e.cp)}); } }); const e0 = merged_list[d3.minIndex(merged_list,d=>d.diff)]; const F = e0.st+Math.exp(R*T)*(e0.cp-e0.pp); const k0i = d3.bisector(d=>d.st).left(merged_list,F)-1; const K0 = merged_list[k0i].st; function mark_0bids(sublist,propname) { let bid0cnt = 0; sublist.forEach((e,i)=>{ const exist = e.hasOwnProperty(propname); const exclude = !exist||e[propname]==0; e.excl=bid0cnt>=2?true:exclude; // all excluded after consecutive 0-bid bid0cnt = !exist? bid0cnt : exclude? bid0cnt+1 : bid0cnt < 2 ? 0 : bid0cnt; }); } mark_0bids(merged_list.slice(0,k0i).reverse(),"pb"); mark_0bids(merged_list.slice(k0i+1),"cb"); const sel = merged_list.filter(e=>!e.excl); sel.forEach((e,i)=>{ e.dk = i==0?(sel[i+1].st-sel[i].st):(i==sel.length-1)?(sel[i].st-sel[i-1].st):(sel[i+1].st-sel[i-1].st)/2; e.mid = (e.st == K0) ? (e.pp+e.cp)/2 : (e.st < K0) ? e.pp : e.cp; e.cont = (e.dk/(e.st**2))*Math.exp(R*T)*e.mid; e.color = (e.st == K0) ? d3.schemeCategory10[4] : e.st < K0 ? d3.schemeCategory10[0] : d3.schemeCategory10[1]; e.label = (e.st == K0) ? "PUT+CALL": e.st < K0 ? "PUT" : "CALL"; }); const sumcont = d3.sum(sel,e=>e.cont); const V = (2/T)*sumcont-(1/T)*(((F/K0)-1)**2); return {sel:sel,K0:K0,F:F,T:T,V:V,VIX:100*Math.sqrt(V),SC:sumcont,Ert:Math.exp(R*T)}; } const result = { near:transform_quote_data(near_quotes.result.optionChain.result[0],(near_quotes.date-currdate)/(365*24*60*60)), next:transform_quote_data(next_quotes.result.optionChain.result[0],(next_quotes.date-currdate)/(365*24*60*60)) } const [t1,t2,te] = [near_quotes.date-currdate,next_quotes.date-currdate,30*24*60*60]; const [T1,T2] = [result.near.T, result.next.T]; const [V1,V2] = [result.near.V, result.next.V]; result.VIX = 100*Math.sqrt( (T1*V1*(t2-te)/(t2-t1) + T2*V2*(te-t1)/(t2-t1))*(365*24*60*60)/te ); return result; }36:T406,function make_table_sel_opts(seldata) { function make_html_strike(d,i) { const color = d3.schemeCategory10[seldata[i].label=="PUT"? 0 : seldata[i].label=="CALL"? 1 : 4]; return html`${d}`; } const max = d3.max(seldata,d=>d.cont); function make_html_contribution(d,i) { return html`

${d.toExponential(1)}

`; } return Inputs.table(seldata, { columns:["label","st","mid","cont"], header:{label:"option",st:"strike(K)",mid:"Q(K)",cont:"C(K)"}, width:{label:40,st:55,mid:40}, format:{ label:d=>d=="PUT+CALL"?"P+C":d, st:(d,i)=>make_html_strike(d,i), mid:d=>d.toFixed(2), cont:(d,i)=>make_html_contribution(d,i) }, maxWidth:305,rows:25}); }37:T68e,function make_table_org_quotes(opttype,orgdata,seldata) { const color = d3.schemeCategory10[opttype=="PUT"?0:1]; const acolor = d3.color(color); acolor.opacity = 0.2; const atxtcolor = d3.color("black"); atxtcolor.opacity = 0.2; const [min,max] = d3.extent(seldata.filter(d=>d.label.includes(opttype)),d=>d.st); function make_html_strike(d,i) { if ( (opttype=="PUT" && orgdata[i].strike < min) || (opttype=="CALL" && orgdata[i].strike > max) ) return html`~~${d}~~`; if ( (opttype=="PUT" && orgdata[i].strike > max) || (opttype=="CALL" && orgdata[i].strike < min) ) return html`${d}`; return html`${d}`; } function make_html_bid_ask(d,i) { const val = d.toFixed(2); if ( (opttype=="PUT" && orgdata[i].strike < min) || (opttype=="CALL" && orgdata[i].strike > max) ) return html`~~${val}~~`; if ( (opttype=="PUT" && orgdata[i].strike > max) || (opttype=="CALL" && orgdata[i].strike < min) ) return html`${val}`; return html`${val}`; } return Inputs.table( orgdata, { columns:["strike","bid","ask"], format:{ strike:(d,i)=>make_html_strike(d,i), bid:(d,i)=>make_html_bid_ask(d,i), ask:(d,i)=>make_html_bid_ask(d,i), }, maxWidth:250, } ); }38:[] 31:{"id":"29c70496eefc97a6","slug":"vix-calculation","title":"호기심 해결 in 주식시장: VIX 계산편","thumbnail":"5eedf25de741ae4c24cce3aa0ed5d06697fd443af29b873e1cdcbb2a6ff08430","access_level":"public","create_time":"$D2024-01-17T23:27:58.054Z","update_time":"$D2024-01-31T13:23:56.435Z","view_time":null,"first_public_time":"$D2024-01-17T23:27:58.054Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"50faa4da52a9ff9b","login":"humble-data-miner","name":"Humble Data Miner","avatar_url":"https://avatars-next.observableusercontent.com/3046b1bea86c5e825baea7c0c403d90ad9690b5396b11b5d02b3a0839fbcb946","tier":"starter_2024"},"version":1222,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"4e2fc41e06361cc3","login":"humble-data-miner","name":"Humble Data Miner","avatar_url":"https://avatars-next.observableusercontent.com/3046b1bea86c5e825baea7c0c403d90ad9690b5396b11b5d02b3a0839fbcb946","tier":null}],"members":[{"type":"individual","id":"4e2fc41e06361cc3","login":"humble-data-miner","name":"Humble Data Miner","avatar_url":"https://avatars-next.observableusercontent.com/3046b1bea86c5e825baea7c0c403d90ad9690b5396b11b5d02b3a0839fbcb946","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"ffed4a92f8068ba7","slug":"myth-buster-in-person","title":"Myth Buster in Person","owner":{"id":"50faa4da52a9ff9b","login":"humble-data-miner","name":"Humble Data Miner"}},"type":"notebook","body":{"title":"호기심 해결 in 주식시장: VIX 계산편","cells":[{"id":0,"value":"# 호기심 해결 in 주식시장: VIX 계산편\n\n### VIX가 뭔데? 어떻게 계산하는데?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1161,"value":"---\n## VIX?\n\n> ‘VIX’로 더 잘 알려진 시카고옵션거래소 변동성지수(Chicago Board Options Exchange Volatility Index)는 미국 증시의 기대 변동성 지표입니다.\n>\n> VIX는 S&P 500 지수의 옵션 가격에 기초하며, 향후 30일간 지수의 풋옵션과 콜옵션 가중 가격을 결합하여 산정합니다.\n> \n> VIX는 향후 미국 주식시장 변동성에 대한 투자자의 견해를 반영하도록 설계되었습니다. 다시 말해, 향후 30일간 S&P 500지수가 얼마나 변동할 것으로 투자자들이 생각하는지를 반영합니다.\n> \n> 시장의 ‘공포 지수’로 지칭되는 경우가 많은 VIX는 투자자들이 투자 결정을 내리기 전에 시장 리스크, 공포 및 스트레스를 측정하는 데 사용합니다.\n>\n>>

- [VIX변동성 지수에 대하여 투자자가 알아야 할 것들](https://www.fidelity.co.kr/insight-and-learning/learn-about-investing/what-is-volatility/volatility-index), 피델리티자산운용코리아(주)

\n\n## 용어정리\n\n* PUT/CALL옵션: 만기안에 자산을 특정가격으로 매도/매수할수 있는 행사권리\n* Strike(K): 옵션에 지정된 행사가격\n* Bid/Ask: 매도/매수호가\n* ITM(In-The-Money): 현재 옵션을 행사해 이익을 볼수 있는 상태\n* OTM(Out-of-The-Money): 현재 옵션을 행사해 이익을 볼수 없는 상태\n * 현재 자산가가 4800라면, 4800미만의 행사가를 가진 모든 PUT 옵션\n * 현재 자산가가 4800라면, 4800초과의 행사가를 가진 모든 CALL 옵션\n * 자산가격의 변동에 따라 ITM이 될 가능성 ∝ 변동성,만기까지 남은시간","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":346,"value":"$33","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1061,"value":"## 위에 서술한 \"VIX 계산과정\" 시각화","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":879,"value":"\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n

N₁=${dates[1].toISOString().split(\"T\")[0]}		N₂=${dates[2].toISOString().split(\"T\")[0]}
${make_table_org_quotes(\"PUT\",tables.PUT1,tables.SEL1)}	${make_table_sel_opts(tables.SEL1)}	${make_table_org_quotes(\"PUT\",tables.PUT2,tables.SEL2)}	${make_table_sel_opts(tables.SEL2)}
${make_table_org_quotes(\"CALL\",tables.CALL1,tables.SEL1)}	${make_table_sel_opts(tables.SEL1)}	${make_table_org_quotes(\"CALL\",tables.CALL2,tables.SEL2)}	${make_table_sel_opts(tables.SEL2)}

\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":352,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1070,"value":"---\n\n## 공식 분해하기\n* ${tex`\\sigma^2=\\frac{2}{T}\\sum_{i}\\frac{\\Delta k}{K_i}e^{RT}Q\\left(K_i\\right) - \\frac{1}{T}\\left[\\frac{F}{K_0}-1\\right]^2`}\n * ${tex`\\frac{1}{T}`}: 연변동률로 변환(Annualize)\n * ${tex`\\frac{\\Delta k}{K_i}e^{RT}Q\\left(K_i\\right)`}\n * ${tex`e^{RT}`}: 옵션가격의 무위험상승률 보정\n * ${tex`{\\Delta k} Q\\left(K_i\\right)`}: 옵션가격×인접옵션간너비=그래프의옵션사각형너비\n * ${tex`\\frac{1}{K_i}`}: 행사가에 따른 옵션가격 정규화(기본적인 옵션가격모델에 근거)\n * 실물,행사가 모두 4800일때 옵션가격이 64 이라면\n * 실물,행사가 모두 2400인 상황에서 추정 옵션가격은 16 이고\n * 실물,행사가 모두 1200인 상황에서 추정 옵션가격은 4 이다\n * ${tex`\\left[\\frac{F}{K_0}-1\\right]^2`}: F(이론기준가)과 K₀(실제기준가)의 차이로 발생하는 추가변동분\n\n

\n## 주목할만한 점\n* PUT옵션의 꼬리가 CALL옵션의 꼬리보다 길다\n * 실물가격이 급격히 떨어져 그보다 비싼 가격에 매도할 가능성 > 실물가격이 다소 올라 그보다 싼가격에 매수할 가능성\n * 시장 참가자들이 가격변동의 상한보다는 하한이 더 크다고 보는 상황\n* 공포지수로써의 VIX\n * VIX의 원래 취지는 SPX(S&P500)지수의 변동성 측정\n * 큰 변동성이 시장의 하락이나 하향매도세를 의미하는것은 아님\n * 하지만 실제 VIX값 계산의 큰 비중이 저가 PUT스프레드에 몰려있음\n * 지수의 상승보다는 하락예상에 훨씬 민감하게 반응함","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1139,"value":"---\n## 참고자료\n* [VIX변동성 지수에 대하여 투자자가 알아야 할 것들](https://www.fidelity.co.kr/insight-and-learning/learn-about-investing/what-is-volatility/volatility-index),피델리티자산운용코리아(주)\n* SPX 옵션 호가자료(지연공시) 출처\n * [Cboe - SPX delayed quotes](https://www.cboe.com/delayed_quotes/spx/quote_table)\n * [Yahoo finance - ^SPX options](https://finance.yahoo.com/quote/%5ESPX/options?p=%5ESPX)\n* Cboe VIX PDF 문서\n * [Volatility Index® Methodology: Cboe Volatility Index®](https://cdn.cboe.com/api/global/us_indices/governance/VIX_Methodology.pdf)\n * [Cboe Volatility Index® Mathematics Methodology](https://cdn.cboe.com/api/global/us_indices/governance/Cboe_Volatility_Index_Mathematics_Methodology.pdf)\n* VIX계산의 이론적 근거\n * [K Demeterfi et al., 1999, More than you ever wanted to know about volatility swaps, Quantitative Strategies Research Notes](http://emanuelderman.com/wp-content/uploads/1999/02/gs-volatility_swaps.pdf)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":1221,"value":"---\n## 부연설명 동영상\n\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":7,"value":"---\n## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":12,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":919,"value":"tables = ({\n PUT1:near_quotes.result.optionChain.result[0].options[0].puts,\n PUT2:next_quotes.result.optionChain.result[0].options[0].puts,\n CALL1:near_quotes.result.optionChain.result[0].options[0].calls,\n CALL2:next_quotes.result.optionChain.result[0].options[0].calls,\n SEL1:data.near.sel,\n SEL2:data.next.sel,\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":230,"value":" near_quotes = {\n let next_term = currdate + 24*24*60*60;\n let res = await fetch_option_quotes(next_term);\n while(res.optionChain.result[0].strikes.length==0) {\n next_term += 24*60*60;\n res = await fetch_option_quotes(next_term);\n }\n return {date:next_term,result:res};\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":252,"value":" next_quotes = {\n let next_term = currdate + 31*24*60*60;\n let res = await fetch_option_quotes(next_term);\n while(res.optionChain.result[0].strikes.length==0) {\n next_term += 24*60*60;\n res = await fetch_option_quotes(next_term);\n }\n return {date:next_term,result:res};\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":227,"value":"function fetch_option_quotes(exp) {\n const url = `https://query1.finance.yahoo.com/v6/finance/options/%5ESPX?date=${exp}&straddle=false&corsDomain=finance.yahoo.com`;\n console.log(url);\n return fetchp(url)\n .then(response => {\n if (!response.ok) { throw new Error(response.status); }\n return response.json();\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"R = {\n const cd = new Date(currdate*1000);\n const url = `https://home.treasury.gov/resource-center/data-chart-center/interest-rates/pages/xmlview?data=daily_treasury_yield_curve&field_tdr_date_value_month=${cd.getFullYear()}${String(cd.getMonth()+1).padStart(2,'0')}`;\n const xml = await d3.xml(url);\n return parseFloat(xml.querySelector(\"entry:last-of-type\").querySelector(\"BC_1MONTH\").textContent)/100;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":62,"value":"currdate = Math.floor(Date.now()/(24*60*60*1000))*(24*60*60);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":265,"value":"dates = [new Date(currdate*1000), new Date(near_quotes.date*1000), new Date(next_quotes.date*1000)]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"import {fetchp} from '@tomlarkworthy/fetchp'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1016,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":973,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":570,"value":"svg_defs_arrow = {\n const svg = d3.create('svg').attr('viewBox', [0, 0, width, 10]);\n \n const markerBoxWidth=6;\n const markerBoxHeight=6;\n const refX = markerBoxWidth;\n const refY = markerBoxHeight/2;\n // See https://developer.mozilla.org/en-US/docs/Web/SVG/Element/marker\n svg\n .append('defs')\n .append('marker')\n .attr('id', 'arrow')\n .attr('viewBox', [0, 0, markerBoxWidth, markerBoxHeight])\n .attr('refX', refX)\n .attr('refY', refY)\n .attr('markerWidth', markerBoxWidth)\n .attr('markerHeight', markerBoxHeight)\n .attr('orient', 'auto-start-reverse')\n .append('path')\n .attr('d', d3.line()([[0,0],[0,markerBoxHeight],[markerBoxWidth,markerBoxHeight/2]]))\n .attr('stroke', 'black');\n\n svg.append(\"path\").attr(\"marker-end\",\"url(#arrow)\").attr(\"fill\",\"none\").attr(\"stroke\",\"black\").attr(\"d\",`M 0 5 h ${width}`);\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W38","stdlib":"1","titling":"auto"}} 32:"$31:body"