使用 Quantlib、Heston 模型定价

如何解决使用 Quantlib、Heston 模型定价

我最近开始探索 Python 的 QuantLib 期权定价库，但遇到了一个我似乎不明白的错误。基本上，我正在尝试使用 Heston 模型为期权定价。我编写的代码取自网上找到的示例，并根据我的具体情况进行了调整。本质上，问题是当我运行下面的代码时，我得到一个错误，我认为是在代码的最后一行触发的，即 european_option.NPV() 函数。

有人可以解释一下我做错了什么吗？

def call_heston(asset,strike,r_daily):
    initial_date = asset.index[0].strftime("%Y-%m-%d")
    final_date = asset.index[-1].strftime("%Y-%m-%d")

    initial_price = asset[0]

    kappa_h = kappa(asset)
    theta_h = asset.std()
    lambda_h = lambd(asset)
    rho_h = rho(asset,kappa_h,theta_h,lambda_h,r_daily)

    maturity_ql = ql.Date(final_date,"%Y-%m-%d")

    payoff = ql.PlainVanillaPayoff(ql.Option.Call,strike)
    exercise = ql.EuropeanExercise(maturity_ql)
    european_option = ql.VanillaOption(payoff,exercise)

    initial_date = ql.Date(initial_date,"%Y-%m-%d")
    ql.Settings.instance().evaluationDate = initial_date

    spot_handle = ql.QuoteHandle(ql.SimpleQuote(initial_price))

    flat_ts = ql.YieldTermStructureHandle(ql.FlatForward(initial_date,r_daily,ql.Actual365Fixed()))

    dividend_yield = ql.YieldTermStructureHandle(ql.FlatForward(initial_date,ql.Actual365Fixed()))

    heston_process = ql.HestonProcess(flat_ts,dividend_yield,spot_handle,rho_h)

    engine = ql.AnalyticHestonEngine(ql.HestonModel(heston_process),0.01,1000)
    european_option.setPricingEngine(engine)

    return european_option.NPV()

call_H_price = call_heston(asset,r_daily)
print("C_0 =",call_H_price)

错误：

RuntimeError                              Traceback (most recent call last)
<ipython-input-19-b6ab40eefd8f> in <module>
     32     return european_option.NPV()
     33 
---> 34 call_H_price = call_heston(asset,r_daily)
     35 print("C_0 =",call_H_price)

<ipython-input-19-b6ab40eefd8f> in call_heston(asset,r_daily)
     27     heston_process = ql.HestonProcess(flat_ts,rho_h)
     28 
---> 29     engine = ql.AnalyticHestonEngine(ql.HestonModel(heston_process),1000)
     30     european_option.setPricingEngine(engine)
     31 

~/opt/anaconda3/lib/python3.8/site-packages/QuantLib/QuantLib.py in __init__(self,process)
  11728 
  11729     def __init__(self,process):
> 11730         _QuantLib.HestonModel_swiginit(self,_QuantLib.new_HestonModel(process))
  11731 
  11732     def theta(self):

RuntimeError: -0.0010463: invalid value