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Issue: Volume 13/Number 4, Summer 2010
Research Papers
Numerical techniques for the valuation of basket options and their Greeks
In this paper, an efficient approach for the computation of the fair value of a basket option as well as its Greeks is presented. Both European and American options are considered; the determination of the price of the former leads to the solution of a parabolic partial differential equation, whereas for the latter a variational inequality needs to be solved. The variational formulations are discretized in terms of finite differences in time and finite elements in space. By enforcing the inequality constraints of the American option via Lagrange multipliers, the discrete inequality can be refo ... |
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Issue: Volume 13/Number 4, Summer 2010
Research Papers
Unbiased Monte Carlo valuation of lookback, swing and barrier options with continuous monitoring under variance gamma models
We introduce fast and unbiased methods for Monte Carlo valuation of lookback, swing, and barrier options under variance gamma models. For the valuation of lookback and swing options, a procedure to draw samples of the final value, infimum, and supremum of variance gamma processes with an additional drift term up to arbitrary precision is developed; for barrier options, a separate method is designed to improve the performance by exploiting the particular payout structure. All algorithms substantially rely on adaptive difference-of-gammas bridge sampling, a newly introduced enhancement of the tr ... |
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Issue: Volume 13/Number 4, Summer 2010
Research Papers
Calibrating volatility function bounds for an uncertain volatility model
It is widely acknowledged that the Black-Scholes constant volatility model is inadequate in modeling the underlying asset price, as evidenced by the observed volatility smile. Based on the relative-entropy minimization method in Avellaneda et al (1997), we propose a method to calibrate, from market bids and asks, a pair of volatility functions for an uncertain volatility model. The mid-prices are used to ensure separation of the lower and upper volatility functions. We show that the calibrated uncertain volatility model produces more realistic bid and ask prices, when compared with prices obta ... |
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Issue: Volume 13/Number 4, Summer 2010
Research Papers
Pricing and hedging American-style options: a simple simulation-based approach
This paper presents a simple yet powerful simulation-based approach for approximating the values of prices and Greeks (ie, derivatives with respect to the underlying spot prices, such as delta, gamma, etc) for American-style options. This approach is primarily based upon the least squares Monte Carlo (LSM) algorithm and is thus termed the modified LSM (MLSM) algorithm. The key to this approach is that with initial asset prices randomly generated from a carefully chosen distribution, we obtain a regression equation for the initial value function, which can be differentiated analytically to gene ... |
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