International Journal of Theoretical and Applied Finance

In this paper an arbitrage strategy is constructed for the modified Black–Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock prices to be also accounted for in addition to the long range dependence introduced by the fractional Brownian motion. Work has been done previously on this problem for the case with constant "volatility" and without a time change; here these results are extended to the case of stochastic volatility models when the modulator is fractional Brownian motion or a time change of it. (Volatility in fractional Black–Scholes models does not carry the same meaning as in the classic Black–Scholes framework, which is made clear in the text.) Since fractional Brownian motion is not a semi-martingale, the Black–Scholes differential equation is not well-defined sense for arbitrary predictable volatility processes. However, it is shown here that any almost surely continuous and adapted process having zero quadratic variation can act as an integrator over functions of the integrator and over the family of continuous adapted semi-martingales. Moreover it is shown that the integral also has zero quadratic variation, and therefore that the integral itself can be an integrator. This property of the integral is crucial in developing the arbitrage strategy. Since fractional Brownian motion and a time change of fractional Brownian motion have zero quadratic variation, these results are applicable to these cases in particular. The appropriateness of fractional Brownian motion as a means of modeling stock price returns is discussed as well.

We combine methods for portfolio optimization in incomplete markets which are due to Karatzas et al. [6] with methods proposed by Nualart based on Malliavin Calculus to model insider trading within a stochastic volatility model. We compute the optimal portfolio within a certain set of insider strategies for a general stochastic volatility model but also apply the methods to explicit examples. We further discuss how the Heston model fits into this context.

Asset-backed securitization (ABS) is a creative arrangement to raise funds through the issuance of marketable securities backed by predictable future cash flows from revenue-producing assets. This paper proposes two pricing models: structural model and intensity model, to value credit spreads on Singapore ABS bonds. Sensitivity analyses were conducted on the ABS credit spreads by varying the values of the key input variables within a plausible range. The property price volatility and its correlations with risk-less interest rates have been shown to have positive effects on the ABS credit spreads. However, when the market volatility is extremely high, the credit spreads decrease with an increase in the time to maturity. The positive effects of the property price volatility were significantly reduced when credit enhancements were added to the ABS bonds, and the credit risks associated with the correlation variable were fully eliminated in the credit enhanced ABS bonds. The rate of loss recovery in the event of default also has significant impact on the credit risks of the ABS bonds. ABS bonds backed by physical property will likely to have high recovery rates thus reducing the credit risks vis-à-vis non-collateralized bonds.

A large body of empirical work is clear-cut in suggesting that the international post-war inflation experience may be described in terms of switches among multiple regimes. A definite explanation of this stylized fact, however, is still under debate. In this paper, we model an economy composed of a large number of interacting price-setting firms which can replicate the evidence at hand. Interactions emerge as a by-product of consumers' uncertainty on the prices charged by different firms. The underlying Markovian structure possesses a stationary distribution with multiple modes, so that its associated dynamics is characterized by multiple regimes and sudden transitions among them. In particular, for any (almost-fully accommodating) monetary policy reaction function, the existence of a multiplicity of inflation regimes is associated to the information acquisition technology consumers have in searching for the lowest price.

Motivated by stylized statistical properties of interest rates, we propose a modeling approach in which the forward rate curve is described as a stochastic process in a space of curves. After decomposing the movements of the term structure into the variations of the short rate, the long rate and the deformation of the curve around its average shape, this deformation is described as the solution of a stochastic evolution equation in an infinite dimensional space of curves. In the case where deformations are local in maturity, this equation reduces to a stochastic PDE, of which we give the simplest example. We discuss the properties of the solutions and show that they capture in a parsimonious manner the essential features of yield curve dynamics: imperfect correlation between maturities, mean reversion of interest rates, the structure of principal components of forward rates and their variances. In particular we show that a flat, constant volatility structures already captures many of the observed properties. Finally, we discuss parameter estimation issues and show that the model parameters have a natural interpretation in terms of empirically observed quantities.

The aim of this paper is to present a stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black–Scholes equation involving volatility with long-range dependence. We define the stochastic option price as a sum of classical Black–Scholes price and random deviation describing the risk from the random volatility. By using the fact that the option price and random volatility change on different time scales, we derive the asymptotic equation for this deviation involving fractional Brownian motion. The solution to this equation allows us to find the pricing bands for options.

Double barrier options can be statically hedged by a portfolio of single barrier knockin options. The main part of the hedge automatically turns into the desired contract along the double barrier corridor extrema.