Deriving the dependence structure of portfolio credit derivatives using evolutionary algorithms

Even if the correct modeling of default dependence is essential for the valuation of portfolio credit derivatives, for the pricing of synthetic CDOs a one-factor Gaussian copula model with constant and equalpairwise correlationsfor all assets in the reference portfolio has become the standard market model. If this model were a re?ection of market opinion, there wouldn't be the implied correlation smilethatis observedinthe market. Thepurposeof thispaperistoderive a correlation structure from observed CDO tranche spreads. The correlation structure is chosen such that all tranche spreads of the traded CDO can be reproduced. This implied correlation structure can then be used to price o?-market tranches with the same underlying as the traded CDO. Using this approach we can significantly reduce the risk to misprice o?-market derivatives. Due to the complexity of the optimization problem we apply Evolutionary Algorithms. --

A note on the correlation smile

The correct modeling of default dependence is essential for the valuation of multiname credit derivatives. However for the pricing of synthetic CDOs a one-factor Gaussian copula model with constant and equal pairwise correlations, default intensities and recovery rates for all assets in the reference portfolio has become the standard market model. If this model were a reflection of market opinion there wouldn't be the implied correlation smile that is observed in the market. The purpose of this paper is to explain the structure of the smile by discussing the influence of different correlation matrices on CDO spreads. --default risk,CDOs,implied correlation smile,correlation matrx,heterogeneity

Risk preference based option pricing in a fractional Brownian market

We focus on a preference based approach when pricing options in a market driven by fractional Brownian motion. Within this framework we derive formulae for fractional European options using the traditional idea of conditional expectation. The obtained formulae - as well as further results - accord with classical Brownian theory and con?rm economic intuition towards fractional Brownian motion. Furthermore the in?uence of the Hurst parameter H on the price of a European option will be analyzed. --Fractional Brownian motion,Conditional expectation,Risk preference based option pricing,Fractional option pricing,Fractional Greeks

An overreaction implementation of the coherent market hypothesis and option pricing

Inspired by the theory of social imitation (Weidlich 1970) and its adaptation to financial markets by the Coherent Market Hypothesis (Vaga 1990), we present a behavioral model of stock prices that supports the overreaction hypothesis. Using our dynamic stock price model, we develop a two factor general equilibrium model for pricing derivative securities. The two factors of our model are the stock price and a market polarization variable which determines the level of overreaction. We consider three kinds of market scenarios: Risk-neutral investors, representative Bernoulli investors and myopic Bernoulli investors. In case of the latter two, risk premia provide that herding as well as contrarian investor behaviour may be rationally explained and justified in equilibrium. Applying Monte Carlo methods, we examine the pricing of European call options. We show that option prices depend significantly on the level of overreaction, regardless of prevailing risk preferences: Downward overreaction leads to high option prices and upward overreaction results in low option prices. --behavioral finance,coherent market hypothesis,market polarization,option pricing,overreaction,chaotic market,repelling market

A note on the correlation smile

The correct modeling of default dependence is essential for the valuation of multiname credit derivatives. However for the pricing of synthetic CDOs a one-factor Gaussian copula model with constant and equal pairwise correlations, default intensities and recovery rates for all assets in the reference portfolio has become the standard market model. If this model were a reflection of market opinion there wouldn’t be the implied correlation smile that is observed in the market. The purpose of this paper is to explain the structure of the smile by discussing the influence of different correlation matrices on CDO spreads

An overreaction implementation of the coherent market hypothesis and option pricing

Inspired by the theory of social imitation (Weidlich 1970) and its adaptation to financial markets by the Coherent Market Hypothesis (Vaga 1990), we present a behavioral model of stock prices that supports the overreaction hypothesis. Using our dynamic stock price model, we develop a two factor general equilibrium model for pricing derivative securities. The two factors of our model are the stock price and a market polarization variable which determines the level of overreaction. We consider three kinds of market scenarios: Risk-neutral investors, representative Bernoulli investors and myopic Bernoulli investors. In case of the latter two, risk premia provide that herding as well as contrarian investor behaviour may be rationally explained and justified in equilibrium. Applying Monte Carlo methods, we examine the pricing of European call options. We show that option prices depend significantly on the level of overreaction, regardless of prevailing risk preferences: Downward overreaction leads to high option prices and upward overreaction results in low option prices

Controlling Chaos in a Model with Heterogeneous Beliefs

In this paper we generalize a chaos control method developed by Ott, Grebogi and Yorke (1990) to control saddle points in R2 which are embadded in a strange attractor of a chaotic system. Our generalized method admits to control any unstable equilibrium in R2. We apply our findings to control the dynamics of the chaotic asset pricing model of Brock and Hommes (1998). In this model chaotic price movements are caused by heterogenous market participants. We introduce a control authority which trades the risky asset like the other market participants. Using our control approach, it is possible for the authority to stabilize the market price with minimum effort

On Modified Mellin Transforms, Gauss-Laguerre Quadrature, and the Valuation of American Call Options

We extend a framework based on Mellin transforms and show how to modify the approach to value American call options on dividend paying stocks. We present a new integral equation to determine the price of an American call option and its free boundary using modied Mellin transforms. We also show how to derive the pricing formula for perpetual American call options using the new framework. A recovery of a result due to Kim (1990) regarding the optimal exercise price at expiry is also presented. Finally, we apply Gauss-Laguerre quadrature for the purpose of an efficient and accurate numerical valuation