波動(dòng)率模型主要有以下三類

- Local volatility, where the forward/spot price of the underlying solves the SDE dF = sigma(F)F dW for a (deter-
ministic) function sigma. A special model is the CEV model with sigma(F) = sigma_beta * F^(beta-1). Problems are that either one use a fully calibrated model (Dupire's formula) but one no longer has closed formula and the resulting
volatility is unstable; or if one use a given model (such as the CEV model), it is hard to calibrate it to the market smile. In addition,? the sticky Greek phenomenon is amplicated. And the dynamics of the smile is wrong.

-? Jump models, where the underlying solves a jump-diusion equation. Jump models fit the smile very well
in the short-term (because the impact of the jump is essentially in the short run). So they are relevant
for short term options. But, they are not satisfactory for long-term options because there is no volatility
risk (the volatility remains deterministic).

- Stochastic volatility models assume that the volatility is a diffusion process correlated to the spot. It is
easily calibrated and allows for a satisfactory handling of the volatility risk. It is less satisfactory for
short-term options.

?

?

轉(zhuǎn)載于:https://www.cnblogs.com/xispace/p/3399769.html

總結(jié)

以上是生活随笔為你收集整理的波动率的三类模型的全部?jī)?nèi)容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網(wǎng)站內(nèi)容還不錯(cuò)，歡迎將生活随笔推薦給好友。