Convertible bonds with higher loan rate: model, valuation, and optimal strategy. (English) Zbl 1406.91456

Wang, Haiyang; Wu, Zhen

Abstr. Appl. Anal. 2014, Article ID 341519, 9 p. (2014).

Summary: We study the pricing problem for convertible bonds via backward stochastic differential equations (BSDEs). By virtue of reflected BSDEs and Malliavin derivatives, we establish the formulae for the fair price of convertible bonds and the hedging portfolio strategy explicitly. We also obtain the optimal conversion time when there is no dividends-paying for underlying common stocks. Furthermore, we consider the case that the loan rate is higher than riskless interest rate in a financial market, and conclude that it does not affect the price of convertible bonds actually. To illustrate our results, some numerical simulations are given and discussed at last.

MSC:

91G20	Derivative securities (option pricing, hedging, etc.)
91G10	Portfolio theory
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H07	Stochastic calculus of variations and the Malliavin calculus

Keywords:

convertible bond pricing; backward stochastic differential equations; hedging portfolio strategy

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