The optimal geometric mean return is an important property of an asset. As a derivative of the underlying asset, the option also has this property. In this paper, we show that the optimal geometric mean returns of a stock and its option are the same from Kelly criterion. It is proved by using binomial option pricing model and continuous stochastic models with self-financing assumption. A simula...

Optimal stopping is a sub-field of probability theory that is present within mathematical finance, mathematical statistics, stochastic calculus and other disciplines. In mathematical finance, one well known problem is the pricing of an American put option. In this thesis we first give a brief review of some general optimal stopping theory, its connection to free-boundary problems and we then ex...

In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee’s moment formulas for the implied volatility and the tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails of stock price distributions in uncorrelated Hull-White, Stein-Stein, and Hest...

This paper examines the correlation between stock and bond returns. It first documents that the major trends in stock-bond correlation for G7 countries follow a similar reverting pattern in the past forty years. Next, an asset pricing model is employed to show that the correlation of stock and bond returns can be explained by their common exposure to macroeconomic factors. The link between the ...

The extreme volatility of stock market values has been the subject of a large body of literature. Previous research focused on the short run because of a widespread belief that, in the long run, the market reverts to well understood fundamentals. Our work suggests this belief should be questioned as well. First, we show actual dividends cannot account for the secular trends of stock market valu...

Aggregate stock market returns display negative skewness. Firm-level stock returns display positive skewness. The large literature that tries to explain the first stylized fact ignores the second. This paper provides a unified theory that reconciles the two facts. I build a stationary asset pricing model of firm announcement events where firm returns display positive skewness. I then show that ...

This paper provides a model for valuing stocks that takes into account the stochastic processes for earnings and interest rates. Our analysis differs from past research of this type in being applicable to stocks that have a positive probability of zero or negative earnings. By avoiding the singularity at the zero point, our earnings-based pricing model achieves improved pricing performance. The...

This paper presents a simple rational expectations model of intertemporal asset pricing relating instability of stock return characteristics to heterogeneity in investor preferences. Heterogeneity is likely to generate declining aggregate relative risk aversion. This leads to variability in expected asset returns, volatility, and autocorrelation. The stronger this variability is, the more heter...

This paper proposes a consistent approach to the pricing of weather derivatives. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. The growth optimal portfolio, which is interpreted as a world stock index, is used as a benchmark or numeraire such that all benchmarked derivative price processes are martingales. No meas...