DolphinDB计算期权希腊字母
期权中的希腊字母包括Delta、Gamma、Theta、Vega、Rho在内，共五个。一个期权非常宝贵的一个特性，这个特性就叫正Gamma，赚钱的时候速度是越来越快的，亏钱的速度是越来越慢的。期权的价格和三个变量有关系，第一个变量是标的的价格（Delte），第二个是市场的隐含波动率（vega），第三个是时间（Theta）的流逝。期权交易员主要关注期权的这些特性。
通过dolphindb，计算50etf期权执行价为3的看涨和看跌期权的希腊字母。耗时在0.9ms
use options_BS
spot=3.018////现货价格
strike_price=3.//行权价格
maturity=(2022.07.27-2022.06.30)\365.////剩余时间
r=0.0//无风险利率
options_type="C"////看涨期权
options_price=0.08////期权价格
timer greaks=bs_greaks(spot,strike_price,maturity, r,options_type,options_price=options_price)
//////Time elapsed: 0.994 ms
print(round(greaks,4))
/////[0.2164,0.08,0.5521,0.3247,-0.4748,0.0012,2.2269,0.5288,1.6664,0.2028,-0.0013,0.0032]
spot=3.018////现货价格
strike_price=3.//行权价格
maturity=(2022.07.27-2022.06.30)\365.////剩余时间
r=0.0//无风险利率
options_type="P"////看涨期权
options_price=0.0574////期权价格
timer greaks=bs_greaks(spot,strike_price,maturity, r,options_type,options_price=options_price)
//////Time elapsed: 0.995 ms
print(round(greaks,4))
/////[0.2022,0.0574,-0.4458,0.3244,-0.4434,-0.001,2.3814,0.5324,-1.3454,0.2169,-0.0012,0.0032]BS模型的脚本代码如下
module options_BS
/////
def pdfNorm(mean,var,x){
return exp(-square(x -mean) / (2 * square(var))) / (sqrt(2 * pi) * var)
}
def bs_price(options_type, spot, strike, maturity, r, vol, q=0.0){
/*
* options_type:'期权类型 ，C' or 'P'
* spot：现货价，float:
* strike：行权价，float
* maturity：剩余天数，float、int
* r：无风险利率，float
* vol：波动率，float
*/
if (options_type == 'C'){
phi = 1}
else if(options_type == 'P'){
phi = -1
}
else{
print("The Options Type is Wrong!")
return
}
if (vol == 0 or maturity == 0){
return max(0.0, phi * (spot - strike))
}
if (strike == 0){
print('The strike_price price cannot be zero')
}
d1 = (log(spot \strike) + (r + 0.5 * vol * vol) * maturity) \vol \sqrt(maturity)
d2 = d1 - vol * sqrt(maturity)
return phi * spot * cdfNormal(0,1,phi * d1) - phi * strike * exp(-r * maturity) * cdfNormal(0,1,phi * d2)
}
def bs_vega(spot, strike, maturity, r, vol, q=0.0){
/*
* spot：现货价，float:
* strike：行权价，float
* maturity：剩余天数，float、int
* r：无风险利率，float
* vol：波动率，float
*/
d1 = (log(spot \ strike) + (r + vol * vol \ 2.) * maturity) \ (vol * sqrt(maturity))
return spot * sqrt(maturity) * pdfNorm(0,1,d1)
}
def implied_volatility_Newton(options_price, options_type, spot, strike, maturity, r){
/*
* 牛顿法实现期权隐含波动率计算
* *options_price,期权价格，float:
* spot：现货价，float:
* strike：行权价，float
* maturity：剩余天数，float、int
* r：无风险利率，float
* vol：波动率，float
* options_type:'期权类型 ，C' or 'P'
*
*/
if (options_type == 'C'){
phi = 1}
else if(options_type == 'P'){
phi = -1
}
else{
print("The Options Type is Wrong!")
return
}
max_iterations= 100
precision= 1.0e-5
sigma = 0.5
for (i in 1..max_iterations){
price = bs_price(options_type, spot, strike, maturity, r, sigma)
vega = bs_vega( spot, strike, maturity, r, sigma)
diff = options_price - price
if (abs(diff) < precision){
return sigma
}
sigma = sigma + diff / vega
}
return sigma
}
def bs_greaks(spot,strike_price,maturity, r,options_type,vol=NULL,options_price=NULL){
//////
/*
* Black-Scholes
* 针对无分红股票欧式期权，使用dolphindb写的Black - Scholes公式
* 参数：
* spot：现货价，float:
* strike_price：行权价，float
* maturity:剩余天数，折算到年，float、int
* r：无风险利率，float
* volatility：波动率，float
* options_type：期权类型('C'、'P')
*
*/
if (options_type == 'C'){
phi = 1}
else if(options_type == 'P'){
phi = -1}
else{
print("The Options Type is Wrong!")
return
}
if (strike_price==0){
print('The strike_price price cannot be zero')
return
}
if (isValid(options_price)){
/////the option iv
volatility = implied_volatility_Newton(options_price, options_type, spot, strike_price, maturity, r)
///option price: [Call price, Put price]
price=options_price
}
if (isValid(vol)){
/////the option iv
volatility=vol
}
a_ = volatility * sqrt(maturity)
d1_ = (log(spot \strike_price) + (r + 0.5 * volatility * volatility) * maturity) \ a_
d2_ =d1_ - a_
b_ = exp(-(r * maturity))
if (isValid(volatility)){
///option price: [Call price, Put price]
price=iif((volatility == 0 || maturity == 0),max(0.0, phi * (spot - strike_price)),
phi * spot * cdfNormal(0,1,phi * d1_) - phi * strike_price * exp(-r * maturity) *cdfNormal(0,1,phi * d2_))
}
/////the option delta
delta=iif((volatility == 0 || maturity == 0),iif(spot>strike_price,phi,0),phi * cdfNormal(0,1,phi * d1_))
/////the option vega
vega=iif((volatility == 0 || maturity == 0),0,spot * pdfNorm(0,1,d1_) * sqrt(maturity))
/////the option theta: [Call theta, Put theta]
theta= -spot * pdfNorm(0,1,d1_) * volatility \ (2 * sqrt(maturity)) - phi * r * strike_price * b_ * pdfNorm(0,1,d2_)
/////the option rho
rho=phi * strike_price * maturity * b_ * cdfNormal(0,1,phi * d2_)\ 100
/////the option gamma
gamma=pdfNorm(0,1,d1_) \ (spot * a_)
/////exercice_probability
exercice_probability =cdfNormal(0,1,d2_)
//////Delta_money
Delta_money =delta * spot
/////Gamma_money
Gamma_money = gamma * spot * spot * 0.01
////Theta_money
Theta_money =theta \ 365.
/////Vega_money
Vega_money = vega * 0.01
return [volatility,price,delta,vega,theta,rho,gamma,exercice_probability,Delta_money,Gamma_money,Theta_money,Vega_money]
}