Classic option pricing theory values a derivative contract via dynamic delta hedging and treating the contract as redundant relative to the underlying security. Dynamic delta hedging proves highly effective in practice, but the remaining risk is still large because of the practical limits of arbitrage. Derivatives can play primary roles in risk allocation. This paper quantifies the percentage variance reduction of delta hedging on U.S. stock options, proposes a top-down return attribution framework to identify the remaining risk sources of the delta-hedged option investment, and constructs a statistical return factor model to explain the variations of the delta-hedged option returns.

To simultaneously account for the properties of interest-rate term structure and foreign exchange rates within one arbitrage-free framework, we propose a class of multi-currency quadratic models (MCQM) with an (m + n) factor structure in the pricing kernel of each economy. The m factors model the term structure of interest rates. The n factors capture the portion of the exchange rate movement that is independent of the term structure. Our modeling framework represents the first in the literature that not only explicitly allows independent currency movement, but also guarantees internal consistency across all economies without imposing any artificial constraints on the exchange rate dynamics. We estimate a series of multi-currency quadratic models using U.S. and Japanese LIBOR and swap rates and the exchange rate between the two economies. Estimation shows that independent currency factors are essential in releasing the tension between the currency movement and the term structure of interest rates.

This paper examines the interaction between default risk and interest-rate risk in determining the term structure of credit default swap spreads at different industry sectors and credit-rating classes. The paper starts with a parsimonious three-factor interest-rate dynamic term structure and projects the credit spread at each industry sector and rating class to these interest-rate factors while also allowing the projection residual dynamics to depend on the level of the interest-rate factors. Estimation shows that credit risk exhibits intricate dynamic interactions with the interest-rate factors.

We develop a simple robust link between deep out-of-the-money American put options on a company's stock and a credit insurance contract on the company's bond. We assume that the stock price stays above a barrier B before default but drops below a lower barrier A after default, thus generating a default corridor [A,B] that the stock price can never enter. Given the presence of this default corridor, a spread between two co-terminal American put options struck within the corridor replicates a pure credit contract, paying off when and only when default occurs prior to the option expiry.

This paper performs specification analysis on the term structure of variance swap rates on the S&P 500 index and studies the optimal investment decision on the variance swaps and the stock index. The analysis identifies 2 stochastic variance risk factors, which govern the short and long end of the variance swap term structure variation, respectively. The highly negative estimate for the market price of variance risk makes it optimal for an investor to take short positions in a short-term variance swap contract, long positions in a long-term variance swap contract, and short positions in the stock index.

We analyze the specifications of option pricing models based on time‐changed Lévy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process itself. Our estimation of a variety of model specifications indicates that to better capture the behavior of the S&P 500 index options, we need to incorporate a high frequency jump component in the return process and generate stochastic volatilities from two different sources, the jump component and the diffusion component.