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Small-time asymptotics for fast mean-reverting stochastic volatility models
Small-time asymptotics fast mean-reverting stochastic volatility models
2010/10/21
In this paper, we study stochastic volatility models in regimes where the maturity is small but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the...
Asymptotics of Random Contractions
Random contractions random scaling Conditional Tail Expectation
2010/10/21
In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\in (0,1)$. Random contracti...
Approximations and asymptotics of upper hedging prices in multinomial models
Black-Scholes-Barenblatt equation contingent claim Cox-Ross-Rubinstein
2010/10/21
We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show t...
Small-Time Asymptotics of Option Prices and First Absolute Moments
option price absolute moment small-time asymptotics approximation
2010/10/20
We study the leading term in the small-time asymptotics of at-the-money call option prices when the stock price process $S$ follows a general martingale. This is equivalent to studying the first cent...
Asymptotics and Exact Pricing of Options on Variance
Asymptotics Exact Pricing Options Variance
2010/10/19
We consider the pricing of derivatives written on the discrete realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limi...