Pricing and hedging long-term options
TL;DR: In this article, the authors show that differences among alternative models usually may not surface when applied to short-term options, but do so when applying to long-term contracts, and they find that short-and longterm contracts indeed contain different information.
About: This article is published in Journal of Econometrics.The article was published on 2000-01-01. It has received 266 citations till now. The article focuses on the topics: LEAPS & Binomial options pricing model.
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TL;DR: In this paper, the authors extend the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of time-varying intensity, and find that any reasonably descriptive continuous-time model for equity-index returns must allow for discrete jumps with a pronounced negative relationship between return and volatility innovations.
Abstract: This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of time-varying intensity. We find that any reasonably descriptive continuous-time model for equity-index returns must allow for discrete jumps as well as stochastic volatility with a pronounced negative relationship between return and volatility innovations. We also find that the dominant empirical characteristics of the return process appear to be priced by the option market. Our analysis indicates a general correspondence between the evidence extracted from daily equity-index returns and the stylized features of the corresponding options market prices. MUCH ASSET AND DERIVATIVE PRICING THEORY is based on diffusion models for primary securities. However, prescriptions for practical applications derived from these models typically produce disappointing results. A possible explanation could be that analytic formulas for pricing and hedging are available for only a limited set of continuous-time representations for asset returns and risk-free discount rates. It has become increasingly evident that such "classical" models fail to account adequately for the underlying dynamic evolution of asset prices and interest rates. Not surprisingly, the inadequacy of these specifications also shows up in bond and derivatives pricing, where the standard representations falter systematically. For example, the BlackScholes pricing formula, although widely used by practitioners, is well known to produce pronounced and persistent biases in the pricing of options. Devi
916 citations
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TL;DR: In this paper, the authors extend the model-free implied volatility to asset price processes with jumps and develop a simple method for implementing it using observed option prices, and perform a direct test of the informational efficiency of the option market using the model free implied volatility.
Abstract: Britten-Jones and Neuberger (2000) derived a model-free implied volatility under the diffusion assumption. In this article, we extend their model-free implied volatility to asset price processes with jumps and develop a simple method for implementing it using observed option prices. In addition, we perform a direct test of the informational efficiency of the option market using the model-free implied volatility. Our results from the Standard & Poor’s 500 index (SPX) options suggest that the model-free implied volatility subsumes all information contained in the Black-Scholes (B-S) implied volatility and past realized volatility and is a more efficient forecast for future realized volatility.
825 citations
TL;DR: In this paper, the authors introduce a nonparametric test to detect jump arrival times and realized jump sizes in asset prices up to the intra-day level, and demonstrate that the likelihood of misclassification of jumps becomes negligible when using high-frequency returns.
Abstract: This paper introduces a new nonparametric test to detect jump arrival times and realized jump sizes in asset prices up to the intra-day level. We demonstrate that the likelihood of misclassiflcation of jumps becomes negligible when we use high-frequency returns. Using our test, we examine jump dynamics and their distributions in the U.S. equity markets. The results show that individual stock jumps are associated with prescheduled earnings announcements and other company-speciflc news events. Additionally, S&P 500 Index jumps are associated with general market news announcements. This suggests difierent pricing models for individual equity options versus index op
810 citations
Cites background from "Pricing and hedging long-term optio..."
...…proved the existence of jumps and their substantial impact on financial management, from portfolio and risk management to option and bond pricing and hedging (see Merton, 1976; Bakshi et al., 1997, 2000; Bates, 1996; Liu et al., 2003; Naik and Lee, 1990; Duffie et al., 2000, and Johannes, 2004)....
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TL;DR: This paper developed a closed-form option valuation formula for a spot asset whose variance follows a GARCH(p,q) process that can be correlated with the returns of the spot asset.
Abstract: This paper develops a closed-form option valuation formula for a spot asset whose variance follows a GARCH(p,q) process that can be correlated with the returns of the spot asset. It provides the first readily computed option formula for a random volatility model that can be estimated and implemented solely on the basis of observables. The single lag version of this model contains Heston's (1993) stochastic volatility model as a continuous-time limit. Empirical analysis on S&P500 index options shows that the out-of-sample valuation errors from the single lag version of the GARCH model are substantially lower than the ad hoc Black-Scholes model of Dumas, Fleming and Whaley (1998) that uses a separate implied volatility for each option to fit to the smirk/smile in implied volatilties. The GARCH model remains superior even though the parameters of the GARCH model are held constant and volatility is filtered from the history of asset prices while the ad hoc Black-Scholes model is updated every period. The improvement is largely due to the ability of the GARCH model to simultaneously capture the correlation of volatility with spot returns and the path dependence in volatility.
755 citations
TL;DR: In this article, the authors extend the model-free implied volatility to asset price processes with jumps and develop a simple method for implementing it using observed option prices, and perform a direct test of the informational efficiency of the option market using the model free implied volatility.
Abstract: Britten-Jones and Neuberger (2000) derived a model-free implied volatility under the diffusion assumption. In this article, we extend their model-free implied volatility to asset price processes with jumps and develop a simple method for implementing it using observed option prices. In addition, we perform a direct test of the informational efficiency of the option market using the model-free implied volatility. Our results from the Standard & Poor's 500 index (SPX) options suggest that the model-free implied volatility subsumes all information contained in the Black--Scholes (B--S) implied volatility and past realized volatility and is a more efficient forecast for future realized volatility. Copyright 2005, Oxford University Press.
712 citations
References
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TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Abstract: If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as combinations of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants. In particular, the formula can be used to derive the discount that should be applied to a corporate bond because of the possibility of default.
28,434 citations
Additional excerpts
...Take the prominent Black and Scholes (1973) model as an example....
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Book•
12 Sep 2011
TL;DR: In this paper, the authors deduced a set of restrictions on option pricing formulas from the assumption that investors prefer more to less, which are necessary conditions for a formula to be consistent with a rational pricing theory.
Abstract: The long history of the theory of option pricing began in 1900 when the French mathematician Louis Bachelier deduced an option pricing formula based on the assumption that stock prices follow a Brownian motion with zero drift. Since that time, numerous researchers have contributed to the theory. The present paper begins by deducing a set of restrictions on option pricing formulas from the assumption that investors prefer more to less. These restrictions are necessary conditions for a formula to be consistent with a rational pricing theory. Attention is given to the problems created when dividends are paid on the underlying common stock and when the terms of the option contract can be changed explicitly by a change in exercise price or implicitly by a shift in the investment or capital structure policy of the firm. Since the deduced restrictions are not sufficient to uniquely determine an option pricing formula, additional assumptions are introduced to examine and extend the seminal Black-Scholes theory of option pricing. Explicit formulas for pricing both call and put options as well as for warrants and the new "down-and-out" option are derived. The effects of dividends and call provisions on the warrant price are examined. The possibilities for further extension of the theory to the pricing of corporate liabilities are discussed.
9,635 citations
TL;DR: In this paper, a closed-form solution for the price of a European call option on an asset with stochastic volatility is derived based on characteristi c functions and can be applied to other problems.
Abstract: I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the BlackScholes (1973) model. The solution technique is based on characteristi c functions and can be applied to other problems.
7,867 citations
"Pricing and hedging long-term optio..." refers background in this paper
...…Chang (1996), and Merton (1976), (iii) the constant-elasticity-of-variance model of Cox and Ross (1976), (iv) the stochastic-volatility models of Heston (1993), Hull and White (1987), Melino and Turnbull (1990, 1995), Scott (1987), Stein and Stein (1991), and Wiggins (1987), (v) the…...
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TL;DR: In this paper, the authors use an intertemporal general equilibrium asset pricing model to study the term structure of interest rates and find that anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices.
Abstract: This paper uses an intertemporal general equilibrium asset pricing model to study the term structure of interest rates. In this model, anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices. Many of the factors traditionally mentioned as influencing the term structure are thus included in a way which is fully consistent with maximizing behavior and rational expectations. The model leads to specific formulas for bond prices which are well suited for empirical testing. 1. INTRODUCTION THE TERM STRUCTURE of interest rates measures the relationship among the yields on default-free securities that differ only in their term to maturity. The determinants of this relationship have long been a topic of concern for economists. By offering a complete schedule of interest rates across time, the term structure embodies the market's anticipations of future events. An explanation of the term structure gives us a way to extract this information and to predict how changes in the underlying variables will affect the yield curve. In a world of certainty, equilibrium forward rates must coincide with future spot rates, but when uncertainty about future rates is introduced the analysis becomes much more complex. By and large, previous theories of the term structure have taken the certainty model as their starting point and have proceeded by examining stochastic generalizations of the certainty equilibrium relationships. The literature in the area is voluminous, and a comprehensive survey would warrant a paper in itself. It is common, however, to identify much of the previous work in the area as belonging to one of four strands of thought. First, there are various versions of the expectations hypothesis. These place predominant emphasis on the expected values of future spot rates or holdingperiod returns. In its simplest form, the expectations hypothesis postulates that bonds are priced so that the implied forward rates are equal to the expected spot rates. Generally, this approach is characterized by the following propositions: (a) the return on holding a long-term bond to maturity is equal to the expected return on repeated investment in a series of the short-term bonds, or (b) the expected rate of return over the next holding period is the same for bonds of all maturities. The liquidity preference hypothesis, advanced by Hicks [16], concurs with the importance of expected future spot rates, but places more weight on the effects of the risk preferences of market participants. It asserts that risk aversion will cause forward rates to be systematically greater than expected spot rates, usually
7,014 citations
"Pricing and hedging long-term optio..." refers background in this paper
...…interest rate, the spot stock price, and the stock return volatility.2 Speci"cally, let the spot interest rate follow a square-root di!usion of the Cox et al. (1985) type: dR(t)"[h R !i R R(t)] dt#p R JR(t) du R (t), (1) where i R , h R /i R , and p R are respectively the speed of adjustment, the…...
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...2 Speci"cally, let the spot interest rate follow a square-root di!usion of the Cox et al. (1985) type:...
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TL;DR: In this article, an option pricing formula was derived for the more general case when the underlying stock returns are generated by a mixture of both continuous and jump processes, and the derived formula has most of the attractive features of the original Black-Scholes formula.
5,812 citations
"Pricing and hedging long-term optio..." refers background in this paper
...…of Merton (1973) and Amin and Jarrow (1992), (ii) the one-dimensional jump-di!usion/pure-jump models of Bates (1991), Madan and Chang (1996), and Merton (1976), (iii) the constant-elasticity-of-variance model of Cox and Ross (1976), (iv) the stochastic-volatility models of Heston (1993), Hull…...
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