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Expected utility theory has produced abundant analytical results in continuous-time finance, but with very little success for discrete-time models. Assuming the underlying asset price follows a general affine GARCH model which allows for non-Gaussian innovations, our work produces an approximate...
In this paper, we are concerned with the Monte Carlo valuation of discretely sampled arithmetic and geometric average options in the Black-Scholes model and the stochastic volatility model of Heston in high volatility environments. To this end, we examine the limits and convergence rates of...
We show how to price and replicate a variety of barrier-style claims written on the log price X and quadratic variation of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest rates. We model the risky asset as a strictly positive continuous semimartingale...
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