Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black/Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset's return is a deterministic function of the asset price and time. Since the volatility function in their model has an arbitrary specification, the deterministic volatility (DV) option valuation model has the potential of fitting the observed cross-section of option prices exactly. Using a sample of S&P 500 index options during the period June 1988 and December 1993, we attempt to evaluate the economic significance of the implied volatility function by examining the predictive and hedging performance of the DV option valuation model. Discussion draft: September 8, 1995 ____________________________________________...

pp.567-611. Contents

. A partial differential equation method based on using auxiliary variables is described for pricing discretely monitored Asian options with or without barrier features. The barrier provisions can be applied to either the underlying asset or to the average. They may also be of either instantaneous or delayed effect (i.e. Parisian style). Numerical examples demonstrate that this method can be used for pricing floating strike, fixed strike, American, or European options. In addition, examples are provided which indicate that an upstream biased quadratic interpolation is superior to linear interpolation for handling the jump conditions at observation dates. Moreover, it is shown that defining the auxiliary variable as the average rather than the running sum is more rapidly convergent for American-Asian options. Keywords: Asian options, Barrier options, Parisian options, PDE option pricing Running Title: Discrete Asian Barrier Options Acknowledgment: This work was supported by the Nation...

A shout option may be broadly defined as a financial contract which can be modified by its holder according to specified rules. In a simple example, the holder could have the right to set the strike of an option equal to the current value of the underlying asset. In such a case, the holder effectively has the right to select when to take ownership of an at-the-money option. More generally, the holder could have multiple rights along these lines, in some cases with a limit placed on the number of rights which may be exercised within a given time period (e.g. four times per year). The value of these types of contracts can be estimated by solving a system of interdependent linear complementarity problems. This paper describes a general framework for the valuation of complex types of shout options. Numerical issues related to interpolation and choice of timestepping method are considered in detail. Some illustrative examples are provided.

Please do not quote without permission * Chidambaran is visiting at NYU, on leave from Tulane. Lee holds joint appointments at Tulane and HKUST. Trigueros is at Tulane. We are grateful for the comments from participants at seminars at Tulane

Abstract not found

In this thesis we develop the mathematical foundations and present valuation algorithms for an important subset of derivative security products; contracts which allow the investor to modify the payoff which is received at the maturity of the contract according to specified rules. Relevant examples of the contracts are mutual funds with embedded modifiable guarantees, usually referred to as "segregated funds". These effectively consist of the purchase of a mutual fund along with a shout put option. A shout option is an option which allows the holder to reset the strike price during the life of the contract. Typically, the investor is allowed to reset the strike price, or guarantee level, to the current level of the underlying fund. The act of reseting the strike price, is referred to as "shouting". The numerical partial differential equation (PDE) methods presented are robust, extensible and allow us to value a wide variety of shout contracts while making minimal assumptions about the ...

Introduction 1. The asset allocation problem is of both of theoretical interest and practical importance. 2. Geometric Brownian motion and constant elasticity of variance (CEV) process models. 3. Progress we have made. 4. Problems: numerical solution of P.D.E. (or O.D.E.). 2 2 The Merton Problem Assumptions: 1. The short-term interest rate is constant and is known. 2. The stock price follows a geometric Brownian motion process: dS(t) = S(t)dt + oeS(t)dB t 3. The stock pays no dividends or other distributions. 4. There are no transaction costs. 5. Power utility function. Merton's result: C (t) = f ae 1 \Gamma fl \Gamma fl[ ( \Gamma r) 2 2oe 2 (1<F20.7

The bid-offer spread on equity options is a key source of profits for market makers, and a key cost for those trading in the options. Spreads are influenced by dynamic market factors, but is there also a predictable element and can Genetic Programming be used for such prediction? We investigate a standard GP approach and two optimisations — age-layering and a novel crossover operator. If both are beneficial as independent optimisations, will they be mutually beneficial when applied simultaneously? Our experiments show a degree of success in predicting spreads, we demonstrate significant benefits for each optimisation technique used individually, and we show that when both are used together significant detrimental over-fitting can occur.

We would like to thank Sheldon Natenberg for suggesting this topic and providing the rationale for the volume induced strategies investigated in this paper. W e also thank Terrance Skantz for valuable comments on an earlier version of this paper. Errors remain ours alone. A previous version of this paper was presented at the Financial Management Meetings 1998.