A Modified Empirical Martingale Simulation for Financial Derivative Pricing

From Time Series of Returns to Option Prices: The Stochastic Discount Factor Approach

“…In Chorro et al (2010), starting from the fact that the algebraic relation (3.80) remains true if the n-sample .S T;i / i 2f1;:::;ng is generated under P instead of under the EMM Q, the authors proposed a new path to risk neutralization and directly priced European options from the historical distribution of the log-returns and the The standard deviations have been computed using 1,000 independent realizations 25 Using the fact that prices may equivalently be expressed using expectations under the historical probability involving the stochastic discount factor (see (3.12)), Huang (2014) and Huang and Tu (2014) proposed and studied an historical version of the EMS when a risk-neutral model is not conveniently obtained. The price to pay is a computational cost that may be heavy if extra techniques are not used.…”

Hedging Barrier Options in GARCH Models with Transaction Costs

“…On the other hand, the NP, MDEK and MSS methods can be extended to the GARCH framework by incorporating numerical algorithms to compute the prices of the derivatives in the hedging portfolios. For example, the empirical martingale simulation of Duan & Simonato (), the dynamic semiparametric approach of Huang & Guo () and the empirical P ‐martingale simulation of Huang () and Huang & Tu () can accurately compute the derivative prices in the GARCH framework.…”

“…We found that 46 of the 292 observations passed their corresponding barrier prices before expiry. In the process of constructing the MSS and MDEK6 hedging strategies at the initial time and to compute the hedging loss at the first passage time, the values of standard call, binary, and UID options at the initial or the first passage times in , , and were computed by the EPMS method of Huang () and Huang & Tu () under the GARCH model .…”

An Empirical Study on Implied GARCH Models

“…Thus researchers have considered GARCH models with leptokurtic innovations. For example, the GARCH model with standardized t innovations (Bollerslev, 1987), generalized exponential innovations (Nelson, 1991), shifted-gamma innovations (Siu, Tong and Yang, 2004) and double-exponential innovations (Huang, 2011;Huang and Guo, 2011) have been discussed. To evaluate the financial derivatives in GARCH models with leptokurtic innovations, the Esscher transform (Gerber and Shiu, 1994) and the extended Girsanov principle (Elliott and Madan, 1998) are two popular change of measure processes used in practice (Badescu and Kulperger, 2008).…”

“…In order to tackle this problem, Duan and Simonato (1998) proposed an empirical martingale simulation (EMS) method to compute option prices more ef-ficiently by generating random paths of the underlying assets from the risk-neutral model. Since an explicit expression of the risk-neutral model may be difficult to obtain in a complex model, Huang (2011) proposed an empirical P -martingale simulation (EPMS) method, which extends the EMS from the risk-neutral framework to the dynamic P measure. The strong consistency of the EPMS method is established and its efficiency is demonstrated by simulation studies.…”