This paper shows how one can obtain a continuous-time preference-free option pricing model with a path-dependent volatility as the limit of a discrete-time GARCH model. In particular, the continuous-time model is the limit of a discrete-time GARCH model of Heston and Nandi (1997) that allows...

This paper develops a discrete-time two-factor model of interest rates with analytical solutions for bonds and many interest rate derivatives when the volatility of the short rate follows a GARCH process that can be correlated with the level of the short rate itself. Besides bond and bond...

Proposals to introduce derivatives whose payouts are explicitly linked to the volatility of an underlying asset have been around for some time. In response to these proposals, a few papers have tried to develop valuation formulae for volatility derivatives—derivatives that essentially help...

This paper develops a closed-form option pricing formula for a spot asset whose variance follows a GARCH process. The model allows for correlation between returns of the spot asset and variance and also admits multiple lags in the dynamics of the GARCH process. The single-factor (one-lag)...

Valuing financial securities often assumes that the contractual obligations of the security are going to be honored. However, frequently a party to a contract will default on its obligations. Because the contractual features of defaultable securities are usually complex and it is difficult to...

Many financial institutions hold derivative securities in their portfolios, and frequently these securities need to be hedged for extended periods of time. Failure to hedge properly can expose an institution to sudden swings in the values of derivatives, such as options, resulting from large,...

The popular practice of selling market volatility through selling straddles exposes traders and investors to substantial risk, especially in equity markets. The returns can be very lucrative, but the probability of large negative returns far exceeds the probability of large positive returns. In...

Because volatility of the underlying asset price is a critical factor affecting option prices and hedge ratios, the modeling of volatility and its dynamics is of vital interest to traders, investors, and risk managers. This modeling is a difficult task because the path of volatility during the...

Auctions, as selling mechanisms, have existed for well over two thousand years. Today, one of the most important auction markets in the world is that of U.S. Treasury securities; approximately $2 trillion worth of Treasury securities was auctioned in 1995. ; A long-standing debate has been about...

This paper develops a model of asymmetric information in which an investor has information regarding the future volatility of the price process of an asset but not the future asset price. It is shown that there exists an equilibrium in which the investor trades an option on the asset and...