American options and callable bonds under stochastic interest rates and endogenous bankruptcy

Nunes, João Pedro Vidal

doi:10.1007/s11147-010-9058-x

Rev Deriv Res

2010

DOI: 10.1007/s11147-010-9058-x

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American options and callable bonds under stochastic interest rates and endogenous bankruptcy

João Pedro Vidal Nunes

Abstract: American options, Optimal stopping time, Convolutions, Stochastic interest rates, Callable defaultable bonds, G13,

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Optimal exercise of American put options near maturity: A new economic perspective

et al. 2021

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The critical price $$S^{*}\left( t\right) $$ S ∗ t of an American put option is the underlying stock price level that triggers its immediate optimal exercise. We provide a new perspective on the determination of the critical price near the option maturity T when the jump-adjusted dividend yield of the underlying stock is either greater than or weakly smaller than the riskfree rate. Firstly, we prove that $$S^{*}\left( t\right) $$ S ∗ t coincides with the critical price of the covered American put (a portfolio that is long in the put as well as in the stock). Secondly, we show that the stock price that represents the indifference point between exercising the covered put and waiting until T is the European-put critical price, at which the European put is worth its intrinsic value. Finally, we prove that the indifference point’s behavior at T equals $$S^{*}\left( t\right) $$ S ∗ t ’s behavior at T when the stock price is either a geometric Brownian motion or a jump-diffusion. Our results provide a thorough economic analysis of $$S^{*}\left( t\right) $$ S ∗ t and rigorously show the correspondence of an American option problem to an easier European option problem at maturity .

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Optimal exercise of American put options near maturity: A new economic perspective

et al. 2021

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Pricing and static hedging of American-style options under the jump to default extended CEV model

Ruas

Dias

Nunes

2013

Journal of Banking & Finance

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American options and callable bonds under stochastic interest rates and endogenous bankruptcy

Abstract: American options, Optimal stopping time, Convolutions, Stochastic interest rates, Callable defaultable bonds, G13,

Cited by 2 publications

References 54 publications

Optimal exercise of American put options near maturity: A new economic perspective

Optimal exercise of American put options near maturity: A new economic perspective

Pricing and static hedging of American-style options under the jump to default extended CEV model

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