@@ -61,6 +61,16 @@
< li class = "toctree-l3" > < a class = "reference internal" href = "#id5" > 2.2 差分法< / a > < / li >
< / ul >
< / li >
< li class = "toctree-l2" > < a class = "reference internal" href = "#id6" > 3.新增希腊字母指标(利率敏感性指标)< / a > < ul >
< li class = "toctree-l3" > < a class = "reference internal" href = "#delta-r" > 3.1 Delta_r< / a > < / li >
< li class = "toctree-l3" > < a class = "reference internal" href = "#delta-r-1bp" > 3.2 Delta_r(1BP)< / a > < / li >
< li class = "toctree-l3" > < a class = "reference internal" href = "#dv01" > 3.3 DV01< / a > < / li >
< li class = "toctree-l3" > < a class = "reference internal" href = "#gamma-r" > 3.4 Gamma_r< / a > < / li >
< li class = "toctree-l3" > < a class = "reference internal" href = "#gamma-r-1bp" > 3.5 Gamma_r(1BP)< / a > < / li >
< li class = "toctree-l3" > < a class = "reference internal" href = "#vega-r" > 3.6 Vega_r< / a > < / li >
< li class = "toctree-l3" > < a class = "reference internal" href = "#vega-r-1bp" > 3.7 Vega_r(1BP)< / a > < / li >
< / ul >
< / li >
< / ul >
< / li >
< li class = "toctree-l1" > < a class = "reference internal" href = "model.html" > 附录2:期权定价方法概述< / a > < / li >
@@ -221,8 +231,8 @@
< tr class = "row-even" > < td > < p > Delta< / p > < / td >
< td > < p > 设当前标的价格为 < span class = "math notranslate nohighlight" > \(S\)< / span > ,设 < span class = "math notranslate nohighlight" > \(S_\mathrm{u}=S+S_\mathrm{\bigtriangleup},S_\mathrm{d}=S-S_\mathrm{\bigtriangleup}\)< / span > < / p >
< p > 将 < span class = "math notranslate nohighlight" > \(S_\mathrm{u}和S_\mathrm{d}\)< / span > 代入定价公式, 得到期权价值 < span class = "math notranslate nohighlight" > \(V_\mathrm{u}和V_\mathrm{d}\)< / span > ; 则< / p >
< p > < span class = "math notranslate nohighlight" > \(Delta=(V_\mathrm{u}-V_\mathrm{d})/(S*0.01 )\)< / span > < / p >
< p > 系统中 < span class = "math notranslate nohighlight" > \(S_\mathrm{\bigtriangleup}\)< / span > 为 < span class = "math notranslate nohighlight" > \(0.005*S \)< / span > < / p >
< p > < span class = "math notranslate nohighlight" > \(Delta=(V_\mathrm{u}-V_\mathrm{d})/(2\times S_\mathrm{\bigtriangleup} )\)< / span > < / p >
< p > 系统中 < span class = "math notranslate nohighlight" > \(S_\mathrm{\bigtriangleup}\)< / span > 为 < span class = "math notranslate nohighlight" > \(0.0001 \)< / span > (绝对偏移,对应1bp) < / p >
< / td >
< / tr >
< tr class = "row-odd" > < td > < p > DeltaCash< / p > < / td >
@@ -232,7 +242,7 @@
< td > < p > 设当前标的价格为 < span class = "math notranslate nohighlight" > \(S\)< / span > , 期权理论价值为 < span class = "math notranslate nohighlight" > \(V\)< / span > ; 设 < span class = "math notranslate nohighlight" > \(S_\mathrm{u}=S+S_\mathrm{\bigtriangleup},S_\mathrm{d}=S-S_\mathrm{\bigtriangleup}\)< / span > < / p >
< p > 将 < span class = "math notranslate nohighlight" > \(S_\mathrm{u}和S_\mathrm{d}\)< / span > 代入定价公式,得到期权价值 < span class = "math notranslate nohighlight" > \(V_\mathrm{u}和V_\mathrm{d}\)< / span > ; 则< / p >
< p > < span class = "math notranslate nohighlight" > \(Gamma=(V_\mathrm{u}+V_\mathrm{d}-2V)/S_\mathrm{\bigtriangleup}^2\)< / span > < / p >
< p > 系统中 < span class = "math notranslate nohighlight" > \(S_\mathrm{\bigtriangleup}\)< / span > 为 < span class = "math notranslate nohighlight" > \(0.01*S \)< / span > < / p >
< p > 系统中 < span class = "math notranslate nohighlight" > \(S_\mathrm{\bigtriangleup}\)< / span > 为 < span class = "math notranslate nohighlight" > \(0.0001 \)< / span > (绝对偏移,对应1bp) < / p >
< / td >
< / tr >
< tr class = "row-odd" > < td > < p > GammaCash< / p > < / td >
@@ -242,7 +252,7 @@
< td > < p > 设当前波动率为𝜎, 设 < span class = "math notranslate nohighlight" > \(𝜎 _\mathrm{u}=𝜎 +𝜎 _\mathrm{\bigtriangleup},𝜎 _\mathrm{d}=𝜎 -𝜎 _\mathrm{\bigtriangleup}\)< / span > < / p >
< p > 将 < span class = "math notranslate nohighlight" > \(𝜎 _\mathrm{u}和𝜎_\mathrm{d}\)< / span > 代入定价公式,得到期权价值 < span class = "math notranslate nohighlight" > \(V_\mathrm{u}和V_\mathrm{d}\)< / span > ; 则< / p >
< p > < span class = "math notranslate nohighlight" > \(Vega=V_\mathrm{u}-V_\mathrm{d}\)< / span > < / p >
< p > 系统中 < span class = "math notranslate nohighlight" > \(𝜎 _\mathrm{\bigtriangleup}\)< / span > 为 0.5% < / p >
< p > 系统中 < span class = "math notranslate nohighlight" > \(𝜎 _\mathrm{\bigtriangleup}\)< / span > 为 0.0001(绝对偏移,对应1bp) < / p >
< / td >
< / tr >
< tr class = "row-odd" > < td > < p > Theta< / p > < / td >
@@ -255,21 +265,170 @@
< / td >
< / tr >
< tr class = "row-even" > < td > < p > Rho< / p > < / td >
< td > < p > 设无风险利率为 < span class = "math notranslate nohighlight" > \(r\)< / span > ,期权理论价值为 < span class = "math notranslate nohighlight" > \(V\)< / span > ; 设 < span class = "math notranslate nohighlight" > \(r_\mathrm{u}=r+10 bp\)< / span > ;< / p >
< td > < p > 设无风险利率为 < span class = "math notranslate nohighlight" > \(r\)< / span > , 期权理论价值为 < span class = "math notranslate nohighlight" > \(V\)< / span > ; 设 < span class = "math notranslate nohighlight" > \(r_\mathrm{u}=r+1bp\)< / span > ;< / p >
< p > 将 < span class = "math notranslate nohighlight" > \(r_\mathrm{u}\)< / span > 代入定价公式,得到期权价值 < span class = "math notranslate nohighlight" > \(V_\mathrm{u}\)< / span > ;则< / p >
< p > < span class = "math notranslate nohighlight" > \(Rho=( V_\mathrm{u}-V)/10bp \)< / span > < / p >
< p > < span class = "math notranslate nohighlight" > \(Rho = V_\mathrm{u} - V \)< / span > < / p >
< / td >
< / tr >
< tr class = "row-odd" > < td > < p > 亚式期权Delta < / p > < / td >
< td > < p > 设当前已观察到的标的平均价格为 < span class = "math notranslate nohighlight" > \(S_\mathrm{A}\) < / span > , 设 < span class = "math notranslate nohighlight" > \(S_\mathrm{A_\mathrm{u}}=S_\mathrm{A}+S_\mathrm{A_\mathrm{\bigtriangleup}}\) < / span > < / p >
< p > 将 < span class = "math notranslate nohighlight" > \(S_\mathrm{A_\mathrm{u}}\)< / span > 代入定价公式,得到期权价值 < span class = "math notranslate nohighlight" > \(V_\mathrm{u}\)< / span > ; 则< / p >
< p > < span class = "math notranslate nohighlight" > \(Delta=(V_\mathrm{u}-V)/S_\mathrm{A_\mathrm{\bigtriangleup}}\)< / span > < / p >
< p > 系统中 < span class = "math notranslate nohighlight" > \(S_\mathrm{A_\mathrm{\bigtriangleup}}\)< / span > 为 < span class = "math notranslate nohighlight" > \(0.01*S_\mathrm{A}\)< / span > < / p >
< / td >
< tr class = "row-odd" > < td > < p > RhoQ < / p > < / td >
< td > < p > 计算逻辑同 Rho < / p > < / td >
< / tr >
< / tbody >
< / table >
< / section >
< section id = "id6" >
< span id = "new-greeks" > < / span > < h2 > 3.新增希腊字母指标(利率敏感性指标)< a class = "headerlink" href = "#id6" title = "Permalink to this headline" > < / a > < / h2 >
< div class = "admonition note" >
< p class = "admonition-title" > Note< / p >
< p > 以下指标< strong > 仅适用于< / strong > 利率收益率、利率债/信用债/其他债券、债券指数、国债期货四类资产。其他资产类别< strong > 不计算< / strong > 这些指标,数值留空。< / p >
< / div >
< section id = "delta-r" >
< h3 > 3.1 Delta_r — 期权对利率的敏感性< a class = "headerlink" href = "#delta-r" title = "Permalink to this headline" > < / a > < / h3 >
< table class = "docutils align-default" >
< colgroup >
< col style = "width: 20%" / >
< col style = "width: 15%" / >
< col style = "width: 65%" / >
< / colgroup >
< thead >
< tr class = "row-odd" > < th class = "head" > < p > 资产类型< / p > < / th >
< th class = "head" > < p > 代表标的< / p > < / th >
< th class = "head" > < p > 公式< / p > < / th >
< / tr >
< / thead >
< tbody >
< tr class = "row-even" > < td > < p > 利率收益率< / p > < / td >
< td > < p > GB10< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Delta\_r = -Delta\)< / span > < / p > < / td >
< / tr >
< tr class = "row-odd" > < td > < p > 利率债/信用债/其他债券< / p > < / td >
< td > < p > 210210.IB< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Delta\_r = Delta \times P \times D\)< / span > < / p > < / td >
< / tr >
< tr class = "row-even" > < td > < p > 债券指数< / p > < / td >
< td > < p > CBA00621.CS< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Delta\_r = Delta \times P \times D\)< / span > < / p > < / td >
< / tr >
< tr class = "row-odd" > < td > < p > 国债期货< / p > < / td >
< td > < p > TS2609< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Delta\_r = Delta \times P \times D / CF\)< / span > < / p > < / td >
< / tr >
< / tbody >
< / table >
< div class = "admonition note" >
< p class = "admonition-title" > Note< / p >
< ul class = "simple" >
< li > < p > < strong > P< / strong > :债券/债券指数在计算日的全价/价格< / p > < / li >
< li > < p > < strong > D< / strong > :债券/债券指数在计算日的修正久期(债券指数使用平均市值法久期)< / p > < / li >
< li > < p > < strong > CF< / strong > :国债期货对应CTD债券的转换因子< / p > < / li >
< / ul >
< / div >
< / section >
< section id = "delta-r-1bp" >
< h3 > 3.2 Delta_r(1BP) — 利率变动1BP时Delta_r的变动< a class = "headerlink" href = "#delta-r-1bp" title = "Permalink to this headline" > < / a > < / h3 >
< p > 适用于全部四种资产类型:< / p >
< p > < span class = "math notranslate nohighlight" > \(Delta\_r(1BP) = Delta\_r \times 0.0001\)< / span > < / p >
< / section >
< section id = "dv01" >
< h3 > 3.3 DV01 — 利率变动1BP时期权价值变动(基点价值)< a class = "headerlink" href = "#dv01" title = "Permalink to this headline" > < / a > < / h3 >
< p > 适用于全部四种资产类型,与 Delta_r(1BP) 等价:< / p >
< p > < span class = "math notranslate nohighlight" > \(DV01 = Delta\_r(1BP)\)< / span > < / p >
< / section >
< section id = "gamma-r" >
< h3 > 3.4 Gamma_r — 期权对利率的二阶敏感性< a class = "headerlink" href = "#gamma-r" title = "Permalink to this headline" > < / a > < / h3 >
< table class = "docutils align-default" >
< colgroup >
< col style = "width: 20%" / >
< col style = "width: 15%" / >
< col style = "width: 65%" / >
< / colgroup >
< thead >
< tr class = "row-odd" > < th class = "head" > < p > 资产类型< / p > < / th >
< th class = "head" > < p > 代表标的< / p > < / th >
< th class = "head" > < p > 公式< / p > < / th >
< / tr >
< / thead >
< tbody >
< tr class = "row-even" > < td > < p > 利率收益率< / p > < / td >
< td > < p > GB10< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Gamma\_r = Gamma\)< / span > < / p > < / td >
< / tr >
< tr class = "row-odd" > < td > < p > 利率债/信用债/其他债券< / p > < / td >
< td > < p > 210210.IB< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Gamma\_r = Delta \times P \times C + (P \times D)^2 \times Gamma\)< / span > < / p > < / td >
< / tr >
< tr class = "row-even" > < td > < p > 债券指数< / p > < / td >
< td > < p > CBA00621.CS< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Gamma\_r = Delta \times P \times C + (P \times D)^2 \times Gamma\)< / span > < / p > < / td >
< / tr >
< tr class = "row-odd" > < td > < p > 国债期货< / p > < / td >
< td > < p > TS2609< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Gamma\_r = Delta \times P \times C / CF + (P \times D / CF)^2 \times Gamma\)< / span > < / p > < / td >
< / tr >
< / tbody >
< / table >
< div class = "admonition note" >
< p class = "admonition-title" > Note< / p >
< ul class = "simple" >
< li > < p > < strong > C< / strong > :债券/债券指数的凸性(债券指数使用平均市值法凸性)< / p > < / li >
< li > < p > P、D、CF 含义同 3.1 节< / p > < / li >
< / ul >
< / div >
< / section >
< section id = "gamma-r-1bp" >
< h3 > 3.5 Gamma_r(1BP) — 利率变动1BP时Gamma_r的变动< a class = "headerlink" href = "#gamma-r-1bp" title = "Permalink to this headline" > < / a > < / h3 >
< p > 适用于全部四种资产类型:< / p >
< p > < span class = "math notranslate nohighlight" > \(Gamma\_r(1BP) = Gamma\_r \times 0.0001^2\)< / span > < / p >
< / section >
< section id = "vega-r" >
< h3 > 3.6 Vega_r — 期权对利率波动率的敏感性< a class = "headerlink" href = "#vega-r" title = "Permalink to this headline" > < / a > < / h3 >
< table class = "docutils align-default" >
< colgroup >
< col style = "width: 20%" / >
< col style = "width: 15%" / >
< col style = "width: 65%" / >
< / colgroup >
< thead >
< tr class = "row-odd" > < th class = "head" > < p > 资产类型< / p > < / th >
< th class = "head" > < p > 代表标的< / p > < / th >
< th class = "head" > < p > 公式< / p > < / th >
< / tr >
< / thead >
< tbody >
< tr class = "row-even" > < td > < p > 利率收益率< / p > < / td >
< td > < p > GB10< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Vega\_r = Vega\)< / span > < / p > < / td >
< / tr >
< tr class = "row-odd" > < td > < p > 利率债/信用债/其他债券< / p > < / td >
< td > < p > 210210.IB< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Vega\_r = Vega \times D \times ytm\)< / span > < / p > < / td >
< / tr >
< tr class = "row-even" > < td > < p > 债券指数< / p > < / td >
< td > < p > CBA00621.CS< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Vega\_r = Vega \times D \times ytm\)< / span > < / p > < / td >
< / tr >
< tr class = "row-odd" > < td > < p > 国债期货< / p > < / td >
< td > < p > TS2609< / p > < / td >
< td > < p > < span class = "math notranslate nohighlight" > \(Vega\_r = Vega \times D \times ytm\)< / span > ( D和ytm使用对应CTD券的值)< / p > < / td >
< / tr >
< / tbody >
< / table >
< div class = "admonition note" >
< p class = "admonition-title" > Note< / p >
< ul class = "simple" >
< li > < p > < strong > ytm< / strong > :债券/债券指数在计算日的到期收益率(债券指数使用平均市值法到期收益率)< / p > < / li >
< li > < p > D 含义同 3.1 节(修正久期)< / p > < / li >
< / ul >
< / div >
< / section >
< section id = "vega-r-1bp" >
< h3 > 3.7 Vega_r(1BP) — 利率波动率变动1BP时Vega_r的变动< a class = "headerlink" href = "#vega-r-1bp" title = "Permalink to this headline" > < / a > < / h3 >
< p > 适用于全部四种资产类型:< / p >
< p > < span class = "math notranslate nohighlight" > \(Vega\_r(1BP) = Vega\_r \times 0.0001\)< / span > < / p >
< / section >
< / section >
< / section >
< / section >