2014/02/09 by Anatoliy Swishchuk, Maksym Tertychnyi, Swishchuk, Anatoliy +4 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60F25 #60H10 #91B70 #Complex Systems and Time Series Analysis #Computational Finance (q-fin.CP) #FOS: Economics and business #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #msc:60F25 #msc:60H10 #msc:91B70 #q-fin.CP #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1402.1953
25 pages, 9 figures
arxiv created 2014/02/09 · openalex publication_date 2014/02/09 · arxiv updated 2014/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of the parameters we find a risk-neural measure and provide new formulas for the distribution of jumps, the mean jump size, and the Poisson process intensity with respect to to this measure. The formulas for a European call foreign exchange option are also derived. We apply these formulas to the case of the log-double exponential distribution of jumps. We provide numerical simulations for the European call foreign exchange option prices with different parameters.