Black-Scholes Formulae for Asian Options in Local Volatility Models
نویسندگان
چکیده
منابع مشابه
Convergence to Black-Scholes for Ergodic Volatility Models
We study the eeect of stochastic volatility on option prices. In the fast-mean reversion model for stochastic volatility of 5], we show that there is a full asymptotic expansion for the option price, centered at the Black-Scholes price. We show, however, that this price does not converge in a strong sense to Black-Scholes as the mean-reversion rate increases. We also introduce a general (possib...
متن کاملUniform Bounds for Black-Scholes Implied Volatility
The Black–Scholes implied total variance function is defined by VBS(k, c) = v ⇔ Φ ( − k/ √ v + √ v/2 ) − eΦ ( − k/ √ v − √ v/2 ) = c. The new formula VBS(k, c) = inf x∈R [ Φ−1 ( c + eΦ(x) ) − x ]2 is proven. Uniform bounds on the function VBS are deduced and illustrated numerically. As a by-product of this analysis, it is proven that F is the distribution function of a logconcave probability me...
متن کاملBlack-scholes and the Volatility Surface
When we studied discrete-time models we used martingale pricing to derive the Black-Scholes formula for European options. It was clear, however, that we could also have used a replicating strategy argument to derive the formula. In this part of the course, we will use the replicating strategy argument in continuous time to derive the Black-Scholes partial differential equation. We will use this...
متن کاملWhen are Options Overpriced ? The Black - Scholes
An important determinant of option prices is the elasticity of the pricing kernel used to price all claims in the economy. In this paper, we rst show that for a given forward price of the underlying asset, option prices are higher when the elasticity of the pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for the ...
متن کاملAsian options and stochastic volatility
In modern asset price models, stochastic volatility plays a crucial role in order to explain several stylized facts of returns. Recently, [3] introduced a class of stochastic volatility models (so called BNS SV model) based on superposition of Ornstein-Uhlenbeck processes driven by subordinators. The BNS SV model forms a flexible class, where one can easily explain heavy-tails and skewness in r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2011
ISSN: 1556-5068
DOI: 10.2139/ssrn.1898992