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Working Paper
Pricing and hedging index options under stochastic volatility: an empirical examination
An empirical examination of the pricing and hedging performance of a stochastic volatility (SV) model with closed form solution (Heston 1993) is provided for options on the S&P 500 index in which the unobservable time varying volatility is jointly estimated with the time invariant parameters of the model. Although, out-of-sample, the mean absolute pricing error in the SV model is always lower than in the Black-Scholes model, still substantial mispricings are observed for deep out-of-the-money options. The degree of mispricing in different options classes is related to bid-ask spreads on ...
Working Paper
Asymmetric information about volatility and option markets
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 expressions for the equilibrium option price and the dynamic trading strategy of the investor are derived endogenously. It is found that the expected volatility of the underlying asset increases in the net order flow in the option market. Also, the depth of the option market is smaller when there is more ...
Journal Article
Issues in hedging options positions
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, unanticipated changes in the levels or volatilities of the underlying asset. Understanding the basic techniques employed for hedging derivative securities and their advantages and pitfalls is therefore of crucial importance. ; This article examines the popular valuation model for options developed by ...
Journal Article
Valuation models for default-risky securities: An overview
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 find comparable securities for which to observe prices, valuation requires formal models that take into account the security's complexities and the uncertainties surrounding future cash flows. Many financial institutions hold large amounts of these securities in their portfolios, and it is important that ...
Journal Article
The risks and rewards of selling volatility
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 fact, selling straddles has resulted in substantial losses at banks and hedge funds such as the former Barings PLC and Long Term Capital Management. ; This article outlines the risks and rewards associated with selling volatility by first examining the statistical properties of the returns generated by ...
Journal Article
Options and volatility
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 life of an option is highly unpredictable. There has been a proliferation of volatility specifications since the original, simple constant-volatility assumption of the famous Black and Scholes option pricing model. This article gives an overview of different specifications of asset price volatility that ...
Working Paper
A discrete-time two-factor model for pricing bonds and interest rate derivatives under random volatility
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 futures, the model yields analytical solutions for prices of European options on discount bonds (and futures) as well as other interest rate derivatives such as caps, floors, average rate options, yield curve options, etc. The advantage of our discrete-time model over continuous-time stochastic volatility ...
Working Paper
Derivatives on volatility: some simple solutions based on observables
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 investors hedge the unpredictable volatility risk. This paper contributes to this nascent literature by developing closed-form/analytical formulae for prices of options and futures on volatility as well as volatility swaps. The primary contribution of this paper is that, unlike all other models, our model ...
Working Paper
Preference-free option pricing with path-dependent volatility: A closed-form approach
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 asymmetry between returns and volatility. For the continuous-time model, one can directly compute closed-form solutions for option prices using the formula of Heston (1993). Toward that purpose, we present the necessary mappings, based on Foster and Nelson (1994), such that one can approximate ...
Journal Article
Treasury auctions: what do the recent models and results tell us?
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 selecting an appropriate auction format for various Treasury securities, a format that would be least subject to possible manipulation by individual traders or a cartel and also result in the highest possible revenues for the Treasury. The Treasury is currently experimenting with what is called a ...