This paper presents a model for option pricing in markets that experience financial crashes. The stochastic differential equation (SDE) of stock price dynamics is coupled to a post-crash market index. The resultant SDE is shown to have stock price and time dependent volatility. The partial differential equation (PDE) for call prices is derived using risk-neutral pricing. European call prices ar...

We consider a (B, S)-security market with standard riskless asset B(t) = B0ert and risky asset S(t) with stochastic volatility depending on time t and the history of stock price over the interval [t − τ, t]. The stock price process S(t) satisfies a stochastic delay differential equation (SDDE) with past-dependent diffusion coefficient. We state some results on option pricing in such a market an...

Pricing options on known-dividend-paying stocks has traditionally been solved by assuming that the stock price minus the present value of dividends follows the lognormal diffusion. The same assumption is also popular in tree methods to avoid combinatorial explosion. Unfortunately, this assumption undervalues the option since the volatility of the underlying stock price is underestimated. The bi...

We investigate the pricing of risk-neutral skewness in the stock options market by creating skewness assets comprised of two option positions (one long and one short) and a position in the underlying stock. The assets are created such that exposure to changes in the underlying stock price (delta) and exposure to changes in implied volatility (vega) are removed, isolating the effect of skewness....

We present results of an experiment on expectation formation in an asset market. Participants to our experiment must provide forecasts of the stock future return to computerized utility-maximizing investors, and are rewarded according to how well their forecasts perform in the market. In the Baseline treatment participants must forecast the stock return one period ahead; in the Volatility treat...

This paper studies the optimal investment strategy of an investor who can access not only the bond and the stock markets, but also the derivatives market. We focus on the investment situation where, in addition to the usual diffusive price shocks, the stock market experiences sudden price jumps and stochastic volatility, and provide closed-form solutions to the dynamic portfolio problem involvi...

True spreads are not directly observable and represent the continuous demand and supply schedule for stock liquidity by heterogeneously informed market participants. Observed spreads are true spreads quantized by minimum market tick size. A regression model of true spreads is developed using spread data from a pure limit order electronic exchange. True spreads are modelled as a continuous posit...

Consumption-based asset pricing models with time-separable preferences can generate realistic amounts of stock price volatility if one allows for small deviations from rational expectations. We consider rational investors who entertain subjective prior beliefs about price behavior that are not equal but close to rational expectations. Optimal behavior then dictates that investors learn about pr...

We investigated the inter-day effects of price limits policies that are employed in agent-based simulations. To isolate the impact of price limits from the impact of other factors, we built an artificial stock market with higher frequency price limits hitting. The trading mechanisms in this market are the same as the trading mechanisms in China's stock market. Then, we designed a series of simu...

We estimate a model of common and commodity-specific, highand low-frequency factors, built on the spline-GARCH model of Engle and Rangel (2008) to explain the period of exceptionally high price volatility in commodity markets during 2006-2008. We find that decomposing realized volatility into highand low-frequency components reveals the impact of slowly-evolving macroeconomic variables on the p...