An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model

This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms

Fixed-income instrument pricing.

In this article we discuss the fundamentals of pricing of the popular financial instruments. The basic point of our approach is to extend the present value benchmark concept. The present value valuation approach plays the similar role as The Newton Laws in the Classic Mechanics. Thus our primary goal is to present a new outlook on valuation of the debt securities and its derivatives. We also, demonstrate why the present value is not a complete method of pricing either securities or derivatives. Then, as illustration we present a valuation of the floating rate, callable and convertible bonds. Next we discuss major drawbacks of the risk neutral interpretation of the derivatives pricing. At the end of the article we discuss interest rate swap and derivative valuation of some classes of the fixed income securities.Bond; coupon bond; present value; floating rate bond; convertible; callable bond; interest rate swap; options valuation; risk neutral probabilities; interest rate derivatives

No-Arbitrage One-Factor Models of the South African Term-Structure of Interest Rates

Short-term interest rate processes determine the term-structure of interest rates in an arbitrage-free market, and are central to the valuation of interest-rate derivatives. We obtain parameter estimates and compare the empirical fit of alternative one-factor continuous-time processes for the South African short-term interest rate (and hence of arbitrage-free term-structure models), using Gaussian estimation methods. We find support only for diffusions where the interest rate volatility is moderately sensitive to the level of the interest rate. Other common models with restrictions that either preclude this effect, or restrict it to be too high, do not fit the data. Differences in the specification of the drift function have no evident effect on model performance.bonds and interest-rate derivatives; arbitrage theory; maximum likelihood; continuous-time short rate models; term-structure of interest rates.

Pricing convertible bonds with equity, interest and credit risk

Imperial Users onl

A Green′s function for a convertible bond using the Vasicek model

We consider a convertible security where the underlying stock price obeys a lognormal random walk and the risk-free rate is given by the Vasicek model. Using a Laplace transform in time and a Mellin transform in the stock price, we derive a Green′s function solution for the value of the convertible bond

On the term structure of Interbank interest rates: jump-diffusion processes and option pricing

In this paper we study the dynamic behavior of the term structure of Interbank interest rates and the pricing of options on interest rate sensitive securities. We posit a generalized single factor model with jumps to take into account external influences in the market. Daily data is used to test for jump effects. Qualitative examination of the linkage between Monetary Authorities interventions and jumps are studied. Pricing results suggests a systematic underpricing in bonds and call options if the jump component is not inc1uded. However, the pricing of put options on bonds presents indeterminacies

Traffic Light Options

This paper introduces, prices, and analyzes traffic light options. The traffic light option is an innovative structured OTC derivative developed independently by several London-based investment banks to suit the needs of Danish life and pension (L&P) companies, which must comply with the traffic light solvency stress test system introduced by the Danish Financial Supervisory Authority (DFSA) in June 2001. This monitoring system requires L&P companies to submit regular reports documenting the sensitivity of the companies’ base capital to certain pre-defined market shocks – the red and yellow light scenarios. These stress scenarios entail drops in interest rates as well as in stock prices, and traffic light options are thus designed to pay off and preserve sufficient capital when interest rates and stock prices fall simultaneously. Sweden’s FSA implemented a traffic light system in January 2006, and supervisory authorities in many other European countries have implemented similar regulation. Traffic light options are therefore likely to attract the attention of a wider audience of pension fund managers in the future. Focusing on the valuation of the traffic light option we set up a Black-Scholes/Hull-White model to describe stock market and interest rate dynamics, and analyze the traffic light option in this framework.Traffic light solvency tests; regulatory solvency requirements; asset-liability management in pension funds; hedging interest rate and stock price risk; derivatives pricing; Black-Scholes/Hull-White model

Fixed-income instrument pricing.

In this article we discuss the fundamentals of pricing of the popular financial instruments. The basic point of our approach is to extend the present value benchmark concept. The present value valuation approach plays the similar role as The Newton Laws in the Classic Mechanics. Thus our primary goal is to present a new outlook on valuation of the debt securities and its derivatives. We also, demonstrate why the present value is not a complete method of pricing either securities or derivatives. Then, as illustration we present a valuation of the floating rate, callable and convertible bonds. Next we discuss major drawbacks of the risk neutral interpretation of the derivatives pricing. At the end of the article we discuss interest rate swap and derivative valuation of some classes of the fixed income securities