In a context of illiquidity, the reservation price is a well-accepted alternative to the usual martingale approach which does not apply. However, this price is not available in closed form and requires numerical methods such as Monte Carlo or polynomial approximations to evaluate it. We show that these methods can be inaccurate and propose a deterministic decomposition of the reservation price using the Lambert function. This decomposition allows us to perform an improved Monte Carlo method, which we name Lambert Monte Carlo (LMC) and to give deterministic approximations of the reservation price and of the optimal strategies based on the Lambert function. We also give an answer to the problem of selecting a hedging asset that minimizes the reservation price and also the cash invested. Our theoretical results are illustrated by numerical simulations.
A Numerical Analysis of the Modified Kirk's Formula and Applications to Spread Option Pricing Approximations a numerical analysis of the modified kirk's formula and applications to spread option pricing approximations
Expansion method for pricing foreign exchange options under stochastic volatility and interest rates
对于没有精确封闭公式的期权，人们提出了一些近似定价的展开方法。Benhamou et al.（2010）提出了智能扩展方法，该方法直接将收益函数的期望值关于波动率的波动率进行扩展，然后将其用于随机波动率模型中的期权定价。本文将他们的方法应用于具有随机利率的随机波动率模型，给出了二阶期权定价的扩展公式。然后进行数值研究，比较我们的近似公式与Monte-Carlo模拟。结果表明，该公式与Grzelak等人（2012）提出的基于特征函数近似的方法在数值上具有可比性。
