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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 237, Pages 256–264
(Mi tm337)
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This article is cited in 5 scientific papers (total in 5 papers)
Perpetual Options for Lévy Processes in the Bachelier Model
É. Mordecki Facultad de Ciencias, Centro de Matemática
Abstract:
A solution to the optimal stopping problem
$V(x)=\sup_\tau\mathsf Ee^{-\delta\tau}g(x+X_\tau)$ is
given, where $X=\{X_t\}_{t\ge 0}$ is a Lévy process, $\tau$ is an
arbitrary stopping time, $\delta\ge 0$ is a discount rate, and the reward
function $g$ takes the form $g_c(x)=(x-K)^+$ or $g_p(x)=(K-x)^+$. The
results interpreted as option prices of perpetual options in Bachelier's
model are expressed in terms of the distribution of the overall supremum in
the case $g=g_c$ and overall infimum in the case $g=g_p$ of the process $X$
killed at rate $\delta$. Closed-form solutions are obtained under mixed
exponentially distributed positive jumps with arbitrary negative jumps for
$g_c$ and under arbitrary positive jumps and mixed exponentially
distributed negative jumps for $g_p$. In the case $g=g_c$, a prophet
inequality comparing the prices of perpetual look-back call options and
perpetual call options is obtained.
Received in November 2001
Citation:
É. Mordecki, “Perpetual Options for Lévy Processes in the Bachelier Model”, Stochastic financial mathematics, Collected papers, Trudy Mat. Inst. Steklova, 237, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 256–264; Proc. Steklov Inst. Math., 237 (2002), 247–255
Linking options:
https://www.mathnet.ru/eng/tm337 https://www.mathnet.ru/eng/tm/v237/p256
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Abstract page: | 237 | Full-text PDF : | 96 | References: | 44 |
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