A General Approach for Lookback Option Pricing under Markov Models

2021/12/01 by Gongqiu Zhang, Zhang, Gongqiu, Lingfei Li +1 · 1 citation
Economics, Econometrics and Finance · Social Sciences · #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Stochastic processes and financial applications #q-fin.CP

paper · pdf · doi:10.48550/arxiv.2112.00439

arxiv created 2021/12/01 · openalex publication_date 2021/12/01 · arxiv updated 2021/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage probabilities. We combine efficient numerical quadrature with continuous-time Markov chain approximation for the first passage problem to price lookbacks. Our method is applicable to a variety of models, including one-dimensional time-homogeneous and time-inhomogeneous Markov processes, regime-switching models and stochastic local volatility models. We demonstrate the efficiency of our method through various numerical examples.

Citations

• The Fine Structure of Asset Returns: An Empirical Investigation
• A Jump-Diffusion Model for Option Pricing

Cited by

• Drawdowns, Drawups, and Occupation Times under General Markov Models

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