International Journal of Theoretical and Applied Finance

Previous work on multifactor term structure models has proposed that the short rate process is a function of some unobserved diffusion process. We consider a model in which the short rate process is a function of a Markov chain which represents the "state of the world". This enables us to obtain explicit expressions for the prices of zero-coupon bonds and other securities. Discretizing our model allows the use of signal processing techniques from Hidden Markov Models. This means we can estimate not only the unobserved Markov chain but also the parameters of the model, so the model is self-calibrating. The estimation procedure is tested on a selection of U.S. Treasury bills and bonds.

We use fuzzy logic engineering tools to detect human behavior in the finance arena, specifically in the technical analysis field. Since technical analysis theory consists of indicators used by experts to evaluate stock prices, the new proposed method maps these indicators into new inputs that can be fed into a fuzzy logic system. This system can create an optimum computerized model to evaluate stock price movement. This method relies on human psychology to predict human behavior when certain price movements or certain price formations occur. The success of the system is measured by comparing system output versus stock price movement. The new stock evaluation method is proven to exceed market performance and it can be an excellent tool in the technical analysis field. The flexibility of the system is also demonstrated.

We present the no-arbitrage price and the hedging strategy of an European contingent claim through a representation formula which is an extension of the Clark-Ocone formula. Our formula can be interpreted as a second order Taylor formula of the no arbitrage price of a contingent claim. The zero order term is given by the mean of the contingent claim payoff, the first order term by the stochastic integral of the mean of its Malliavin derivative and the second order term by the stochastic integral of the conditional expectation of the second Malliavin derivative. A Taylor series expansion is also provided together with a bound to the approximation error obtained by neglecting the second order term in the Taylor formula.

We investigate the effect of stochastic fluctuations of an interest rate on the value of a derivative. We derive the modified Black-Scholes equation that describes evolution of the value of a derivative averaged over an ensemble of stochastic fluctuations of the rate of interest and depends on the "renormalized" values of volatility and rate of interest. We present the explicit expressions for the renormalized volatility and interest rate that incorporate the corrections owing to the short-term stochastic variations of the interest rate. The stochastic component of the interest rate tends to enhance the effective volatility and reduce the effective interest rate that determine an evolution of the option pricing "smoothed out" over the stochastic variations. The results of numerical solution of the modified Black-Scholes equation with the renormalized coefficients are illustrated for an American put option on non-dividend-paying stock.

I present a model of stock market price fluctuations incorporating effects of share supply as a history-dependent function of previous purchases and share demand as a function of price deviation from moving averages. I discuss interpretation of model parameters and of the form of dynamically evolving supply and demand functions. Parameters and dynamic supply and demand functions can be regarded as providing quantitative behavioral characterization of investors within markets. Price charts generated assuming different dynamic supply functions exhibit structure consistent with the hypothesis that dominant investor behavior is different on different time scales.

We describe a robust correction to Black-Scholes American derivatives prices that accounts for uncertain and changing market volatility. It exploits the tendency of volatility to cluster, or fast mean-reversion, and is simply calibrated from the observed implied volatility skew. The two-dimensional free-boundary problem for the derivative pricing function under a stochastic volatility model is reduced to a one-dimensional free-boundary problem (the Black-Scholes price) plus the solution of a fixed boundary-value problem. The formal asymptotic calculation that achieves this is presented here. We discuss numerical implementation and analyze the effect of the volatility skew.

Alternative approaches to hedging swaptions are explored and tested by simulation. Hedging methods implied by the Black swaption formula are compared with a lognormal forward LIBOR model approach encompassing all the relevant forward rates. The simulation is undertaken within the LIBOR model framework for a range of swaptions and volatility structures. Despite incompatibilities with the model assumptions, the Black method performs equally well as the LIBOR method, yielding very similar distributions for the hedging profit and loss — even at high rehedging frequencies. This result demonstrates the robustness of the Black hedging technique and implies that — being simpler and generally better understood by financial practitioners — it would be the preferred method in practice.