389 research outputs found
Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model
Our derivation of the distribution function for future returns is based on
the risk neutral approach which gives a functional dependence for the European
call (put) option price, C(K), given the strike price, K, and the distribution
function of the returns. We derive this distribution function using for C(K) a
Black-Scholes (BS) expression with volatility in the form of a volatility
smile. We show that this approach based on a volatility smile leads to relative
minima for the distribution function ("bad" probabilities) never observed in
real data and, in the worst cases, negative probabilities. We show that these
undesirable effects can be eliminated by requiring "adiabatic" conditions on
the volatility smile
An introduction to multilevel Monte Carlo for option valuation
Monte Carlo is a simple and flexible tool that is widely used in
computational finance. In this context, it is common for the quantity of
interest to be the expected value of a random variable defined via a stochastic
differential equation. In 2008, Giles proposed a remarkable improvement to the
approach of discretizing with a numerical method and applying standard Monte
Carlo. His multilevel Monte Carlo method offers an order of speed up given by
the inverse of epsilon, where epsilon is the required accuracy. So computations
can run 100 times more quickly when two digits of accuracy are required. The
multilevel philosophy has since been adopted by a range of researchers and a
wealth of practically significant results has arisen, most of which have yet to
make their way into the expository literature.
In this work, we give a brief, accessible, introduction to multilevel Monte
Carlo and summarize recent results applicable to the task of option evaluation.Comment: Submitted to International Journal of Computer Mathematics, special
issue on Computational Methods in Financ
The Term Structure of Systematic and Idiosyncratic Risk
We study the term structure of variance (total risk), systematic and idiosyncratic risk. Consistent with the expectations hypothesis, we find that, for the entire market, the slope of the term structure of variance is mainly informative about the path of future variance. Thus, there is little indication of a time-varying term premium. Turning the focus to individual stocks, we cannot reject the expectations hypothesis for the systematic variance, but we strongly reject it for idiosyncratic variance. Our results are robust to jumps and potential statistical biases
Option Pricing Kernels and the ICAPM
We estimate the parameters of pricing kernels that depend on both aggregate wealth and state variables that describe the investment opportunity set, using FTSE 100 and S&P 500 index option returns as the returns to be priced. The coefficients of the state variables are highly significant and remarkably consistent across specifications of the pricing kernel, and across the two markets. The results provide further evidence that, consistent with Merton's (1973) Intertemporal Capital Asset Pricing Model, state variables in addition to market risk are priced
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