Stochastic discount factor

Résumé

The concept of the stochastic discount factor (SDF) is used in financial economics and mathematical finance. The name derives from the price of an asset being computable by "discounting" the future cash flow \tilde{x}_i by the stochastic factor \tilde{m}, and then taking the expectation. This definition is of fundamental importance in asset pricing. If there are n assets with initial prices p_1, \ldots, p_n at the beginning of a period and payoffs \tilde{x}_1, \ldots, \tilde{x}_n at the end of the period (all xs are random (stochastic) variables), then SDF is any random variable \tilde{m} satisfying :E(\tilde{m}\tilde{x}_i) = p_i, \text{for } i=1,\ldots,n. The stochastic discount factor is sometimes referred to as the pricing kernel as, if the expectation E(\tilde{m},\tilde{x}_i) is written as an integral, then \tilde{m} can be interpreted as the kernel function in an integral t

Source officielle

https://en.wikipedia.org/wiki/Stochastic_discount_factor

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Option Pricing with Model-Guided Nonparametric Methods

Loriano Mancini

Parametric option pricing models are largely used in Finance. These models capture several features of asset price dynamics. However, their pricing performance can be significantly enhanced when they are combined with nonparametric learning approaches that learn and correct empirically the pricing errors. In this paper, we propose a new nonparametric method for pricing derivatives assets. Our method relies on the state price distribution instead of the state price density because the former is easier to estimate nonparametrically than the latter. A parametric model is used as an initial estimate of the state price distribution. Then the pricing errors induced by the parametric model are fitted nonparametrically. This model-guided method estimates the state price distribution nonparametrically and is called Automatic Correction of Errors (ACE). The method is easy to implement and can be combined with any model-based pricing formula to correct the systematic biases of pricing errors. We also develop a nonparametric test based on the generalized likelihood ratio to document the efficacy of the ACE method. Empirical studies based on S&P 500 index options show that our method outperforms several competing pricing models in terms of predictive and hedging abilities.

American Statistical Association2009

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We introduce the class of linear-rational term structure models in which the state price density is modeled such that bond prices become linear-rational functions of the factors. This class is highly tractable with several distinct advantages: (i) ensures non-negative interest rates, (ii) easily accommodates unspanned factors affecting volatility and risk premiums, and (iii) admits semi-analytical solutions to swaptions. A parsimonious model specification within the linear-rational class has a very good fit to both interest rate swaps and swaptions since 1997 and captures many features of term structure, volatility, and risk premium dynamics-including when interest rates are close to the zero lower bound.

Wiley2017

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