Damiaan Lemmens | Searcharxiv

arXiv2011

Path integral approach to Asian options in the Black-Scholes model

We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.

q-fin.PR↗

arXiv2011

Path integral approach to the pricing of timer options with the Duru-Kleinert time transformation

In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both the perpetual timer call options and the finite time-horizon timer call options. These general results allow us to find closed-form pricing formulas for both the perpetual and the finite time-horizon timer options under the 3/2 stochastic volatility model as well as under the Heston stochastic volatility model. For the treatment of timer option under the 3/2 model we will rely on the path integral for the Morse potential, with the Heston model we will rely on the Kratzer potential.

q-fin.PR↗