A lattice approach for pricing convertible bond asset swaps with market risk and counterparty risk
This paper proposes a new lattice framework for valuing convertible bonds (CBs) and asset swaps on CBs (CBASs) with market risk and counterparty risk, where interest rate is assumed to follow a mean-reverting square root process. The reduced-form approach is generalized to include a constant elasticity of variance (CEV) process for equity price prior to default. In order to approximate the CEV process while taking into account stochastic interest rate and the correlation between stock price and interest rate, I first propose a transform that is uncorrelated with interest rate, and then construct a new lattice method which can ensure the validity of branching probabilities for all nodes. The lattice framework performs properly when it is used to value European call options. Based on the empirical results in Duffie et al. (J. Fin. Econ. 83(3): 635-665, 2007) and Jankowitsch et al. (J. Bank. Fin. 32(7): 1269-1285, 2008), a novel default intensity process is constructed which is specified as a function of time, stock price, and interest rate. When valuing the asset swaps, the counterparty risk is taken into consideration. Based on the results of the numerical experiments, the impacts of different parameters on the prices of CBs and CBASs are explained.
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