求助各位，要想定价一个 European vanilla call option with stochastic volatility 用哪种方法比较好？为什么？
1, risk - neutral valuation
2, trees
3, fourier methods
4, monte carlo simulation
This question is too general.
To price a Call, or any other derivatives, we need to know what kind of model you want to use, then we will choose which method.
For a stochastic vol model, if we know the characteristic function of assert in a closed form, FFT can be applied to European options, because fourier transformation of price is available. What's more, if we just want to price a call, numerical integraiton works also. The advantage of pricing calls with FFT is that once we use this method, prices for all strikes( precisely almost all) can be obtained without additional computation. I think PDE method can also be taken, but PDE in two dimension is not so competitive w.r.t to FFT.
Risk-Neutral valuation? I am curious why you mentioned it. Don't we price derivatives under risk-neutral proba? And i don't know how to price derivative under sto vol with trees......
MC is a nice candidate to price derivatives, but we all know that it is not so efficient. Especially in your case, i really doute the efficiency of MC comparing to other method. I said I doute, because i never priced derivatives with MC under sto vol models. But one thing i am sure is that FFT and Numerical Integration is very efficient. Here is the articles about methods i talked, hope it helps.
1. FFT
P. Carr and D. Madan. Option valuation using the fast
fourier transform. Journal of Computational Finance,
2(4):6173, 1999
2. N I
M. Attari. Option pricing using fourier transforms:
A numerically efficient simplification. Woring Paper,
Charles River Associates, 2004
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