A Dynamic Programming Approach for Pricing Options Embedded in Bonds

The aim of this paper is to price options embedded in bonds in a Dynamic Programming (DP) framework, the focus being on call and put options with advance notice. The pricing of interest rate derivatives was usually done via trees or finite differences. Trees are not really very efficient as they deform crudely the dynamic of the underlying asset(s), here the short term risk-free interest rate. They can be interpreted as elementary DP procedures with fixed grid sizes. For a long time, finite differences presented poor accuracy because of the discontinuities of the bond's value that may arise at decision dates. Recently, remedies were given by d'Halluin et al (2001) via techniques related to flux limiters. DP does not suffer from discontinuities that may arise at decision dates and does not require a time discretization. It may also be implemented in discrete-time models. Results show efficiency and robustness. Suggestions to combine DP and finite differences are also formulatedDynamic Programming, Stochastic Processes, Options Embedded in Bonds, American Options

© 2004 INFORMS

informs ® doi 10.1287/moor.1040.010

An analysis of the true notional bond system applied to the CBOT T-bond futures

The conversion factor system (CFS) is used in the determination of the invoice price of the Chicago Board of Trade Treasury-bond futures. As an alternative to the CFS, Oviedo [Oviedo, R.A., 2006. Improving the design of Treasury-Bond futures contracts. The Journal of Business 79, 1293-1315] proposed the True Notional Bond System (TNBS), and showed that it outperforms the CFS when interest rates are deterministic. The main purpose of this paper is to compare the effectiveness of the two systems in a stochastic environment. In order to do so, we price the CBOT T-bond futures as well as all its embedded delivery options under both the CFS and the TNBS. Our pricing procedure is an adaptation of the Dynamic Programming algorithm described in Ben-Abdallah et al. [Ben-Abdallah, R., Ben-Ameur, H., Breton, M., 2007. Pricing CBOT Treasury Bond futures. Les Cahiers du GERAD G-2006-77]. Numerical illustrations show that, in a stochastic framework, TNBS does not always outperform the CFS. However, as the long-term mean moves away from the level of the notional rate, the TNBS performs increasingly better than the CFS.Futures Asset pricing Dynamic programming Delivery options

(membre du jury de Concordia University)

Thèse présentée à l

A dynamic programming approach for pricing CDS and CDS options

We propose a flexible framework for pricing single-name knock-out credit derivatives. Examples include Credit Default Swaps (CDSs) and European, American and Bermudan CDS options. The default of the underlying reference entity is modelled within a doubly stochastic framework where the default intensity follows a CIR++ process. We estimate the model parameters through a combination of a cross sectional calibration-based method and a historical estimation approach. We propose a numerical procedure based on dynamic programming and a piecewise linear approximation to price American-style knock-out credit options. Our numerical investigation shows consistency, convergence and efficiency. We find that American-style CDS options can complete the credit derivatives market by allowing the investor to focus on spread movements rather than on the default event.Credit derivatives, Credit default swaps, Bermudan options, Dynamic programming, Doubly stochastic Poisson process, Cox process,

1 A Dynamic Programming Approach to Price Installment Options

Installment options are Bermudan-style options where the holder period-ically decides whether to exercise or not and then to keep the option alive or not (by paying the installment). We develop a dynamic programming pro-cedure to price installment options. We study in particular the Geometric Brownian Motion case and derive some theoretical properties of the IO con-tract within this framework. We also characterize the range of installments within which the installment option is not redundant with the European contract. Numerical experiments show the method yields monotonically converging prices, and satisfactory trade-offs between accuracy and com-putational time. Our approach is finally applied to installment warrants, which are actively traded on the Australian Stock Exchange. Numerical in-vestigation shows the various capital dilution effects resulting from different installment warrant designs