Option valuation with co-integrated asset prices (original) (raw)
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Options on stocks are priced using information on index options and viewing stocks in a factor model as indirectly holding index risk. The method is particularly suited to developing quotations on stock options when these markets are relatively illiquid and one has a liquid index options market to judge the index risk. The pricing strategy is illustrated on IBM and Sony options viewed as holding SPX and Nikkei risk respectively.
Some remarks on two-asset options pricing and stochastic dependence of asset prices É
Social Science Research Network, 2001
In this short note, we consider some problems of two-asset options pricing. In particular, we investigate the relationship between options prices and the 'correlation' parameter in the Black-Scholes model. Then, we consider the general case in the framework of the copula construction of risk-neutral distributions. This extension involves results on the supermodular order applied to the Feynman-Kac representation. We show that it could be viewed as a generalization of a maximum principle for parabolic PDE.
International Journal of Economics and Financial Issues, 2016
This research focuses on the empirical comparative analysis of three models of option pricing: (a) The implied volatility daily calibrated Black–Scholes model, (b) the Cox and Ross univariate model with the volatility which is a deterministic and inverse function of the underlying asset price and (c) the Kou jump diffusion model. To conduct the empirical analysis, we use a diversified sample with options written on three US indexes during 2007: Large cap (Standard and Poor 500 [SP 500]), Hi-Tech cap (Nasdaq 100) and small cap (Russell 2000). For the estimation of models parameters, we opted for the data-fitting technique using the trust region reflective algorithm on option prices, rather than the more common maximum likelihood or generalized method of moments on the history of the underlying asset. The analysis that we conducted clearly shows the supremacy of Kou model. We also notice that it provided better results for the Nasdaq 100 and Russell 2000 index options than for the SP ...
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The Journal of Finance, 1987
This paper proposes an analytical approximation to price exotic options within a stochastic volatility framework. Assuming a general mean reverting process for the underlying asset and a square-root process for the volatility, we derive an approximation for option prices using a Taylor expansion around two average defined volatilities. The moments of the average volatilities are computed analytically at any order using a Frobenius series solution to some ordinary differential equation. Pricing some exotics such as barrier and digital barrier options, the approximation is found to be very efficient and convergent even at low Taylor expansion order.
Stochastic Dominance and Option Pricing in Discrete and Continuous Time: An Alternative Paradigm
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This paper examines option pricing in a universe in which it is assumed that markets are incomplete. It derives multiperiod discrete time option bounds based on stochastic dominance considerations for a risk-averse investor holding only the underlying asset, the riskless asset and (possibly) the option for any type of underlying asset distribution, discrete or continuous. It then considers the limit behavior of these bounds for special categories of such distributions as trading becomes progressively more dense, tending to continuous time. It is shown that these bounds nest as special cases most, if not all, existing arbitrage-and equilibrium-based option pricing models. Thus, when the underlying asset follows a generalized diffusion both bounds converge to a single value. For jumpdiffusion processes, stochastic volatility models, and GARCH processes the bounds remain distinct and define several new option pricing results containing as special cases the arbitrage-based results.
An empirical model of volatility of returns and option pricing
Physica A: Statistical Mechanics and its Applications, 2003
In a seminal paper in 1973, Black and Scholes argued how expected distributions of stock prices can be used to price options. Their model assumed a directed random motion for the returns and consequently a lognormal distribution of asset prices after a finite time. We point out two problems with their formulation. First, we show that the option valuation is not uniquely determined; in particular ,strategies based on the delta-hedge and CAPM (the Capital Asset Pricing Model) are shown to provide different valuations of an option. Second, asset returns are known not to be Gaussian distributed. Empirically, distributions of returns are seen to be much better approximated by an exponential distribution. This exponential distribution of asset prices can be used to develop a new pricing model for options that is shown to provide valuations that agree very well with those used by traders. We show how the Fokker-Planck formulation of fluctuations (i.e., the dynamics of the distribution) can be modified to provide an exponential distribution for returns. We also show how a singular volatility can be used to go smoothly from exponential to Gaussian returns and thereby illustrate why exponential returns cannot be reached perturbatively starting from Gaussian ones, and explain how the theory of 'stochastic volatility' can be obtained from our model by making a bad approximation. Finally, we show how to calculate put and call prices for a stretched exponential density.