Purely Discontinuous Asset Price Processes
نویسنده
چکیده
This paper presents the case for modeling asset price processes as purely discontinuous processes of ̄nite variation with an in ̄nite arrival rate of jumps that have arrival rates completely monotone in the jump size. The arguments address both the empirical realities of asset returns and the implications of the economic principle of no arbitrage. Two classes of economic models meeting these conditions are presented and linked. An important example given by the variance gamma process is studied in detail and used to design optimal derivative investment portfolios that are calibrated to actual portfolios to reverse engineer trader preferences and beliefs and infer personalized risk neutral measures termed position measures. Illustrative comparisons of statistical, risk neutral and position measures are also provided.
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