python - 从 Quantlib BachelierSwaption 价格中检索 Black vol

Question

我想从 Quantlib BachelierSwaptionEngine 计算的掉期期权价格中检索 Black Vol。看起来这可以通过优化器(例如 newton 方法)在 Quantlib 中完成，或者直接通过 impliedVolatility 方法完成。我无法在 Quantlib Python 中使用 Quantlib 优化器或 impliedVolatility 方法。

下面的代码显示了我如何在 Quantlib 中计算掉期期权价格。从那里我需要根据代码中计算的掉期期权价格检索 Black vol

import Quantlib as ql
from scipy import optimize

calc_date = ql.Date(29,3,2019)

rate = ql.SimpleQuote(0.01)
rate_handle = ql.QuoteHandle(rate)
dc = ql.Actual365Fixed()
spot_curve = ql.FlatForward(calc_date, rate_handle, dc)

start = 10
length = 10
start_date =  ql.TARGET().advance(calc_date, start, ql.Years)
maturity_date = start_date + ql.Period(length, ql.Years)
fixed_schedule = ql.Schedule(start_date, maturity_date,
                      ql.Period(1, ql.Years), ql.TARGET(), ql.Unadjusted, 
                      ql.Unadjusted,ql.DateGeneration.Forward, False)
floating_schedule = ql.Schedule(start_date, maturity_date,
                        ql.Period(6, ql.Months), ql.TARGET(), 
                        ql.ModifiedFollowing, ql.ModifiedFollowing,
                        ql.DateGeneration.Forward, True)

index6m = ql.Euribor6M(ql.YieldTermStructureHandle(spot_curve))

rate = 1.45 / 100
swap = ql.VanillaSwap(ql.VanillaSwap.Receiver, 10000000,
               fixed_schedule, rate, ql.Thirty360(ql.Thirty360.BondBasis),
               floating_schedule, index6m, 0.0, index6m.dayCounter())

swap.setPricingEngine(ql.DiscountingSwapEngine( 
ql.YieldTermStructureHandle(spot_curve)))


swaption_normal_model = ql.Swaption(swap, 
  ql.EuropeanExercise(swap.startDate()))


normal_vol = ql.SimpleQuote(0.005266)
swaption_normal_model.setPricingEngine
(ql.BachelierSwaptionEngine(ql.YieldTermStructureHandle(spot_curve), 
ql.QuoteHandle(normal_vol)))
swaption_normal_model_value = swaption_normal_model.NPV()

Answer 1

我使用了 scipy 中的牛顿最小化函数来检索隐含的黑色体积，见下文:

swaption_black_model = ql.Swaption(swap, ql.EuropeanExercise(swap.startDate()))
initial_vol_guess = 0.60


def find_implied_black(vol):
    black_vol = ql.SimpleQuote(vol)
    swaption_black_model.setPricingEngine(
    ql.BlackSwaptionEngine(ql.YieldTermStructureHandle(spot_curve), 
    ql.QuoteHandle(black_vol)))
    swaption_black_model_value = swaption_black_model.NPV()
    diff = swaption_normal_model_value - swaption_black_model_value

    return diff


implied_black_vol = optimize.newton(find_implied_black, initial_vol_guess)
implied_black_vol = ql.SimpleQuote(implied_black_vol)
swaption_black_model.setPricingEngine(
ql.BlackSwaptionEngine(ql.YieldTermStructureHandle(spot_curve), 
ql.QuoteHandle(implied_black_vol)))
swaption_black_model_value = swaption_black_model.NPV()

print('Normal swaption price is {}'.format(swaption_normal_model_value))
print('Black swaption price is {}'.format(swaption_black_model_value))