Optimal Exercise Of Russian Options In The
Binomial Model
Author(s)
R. W. Chen & B. Rosenberg
Abstract
The Russian option is a two-party contract which creates a liability for the option
seller to pay the option buyer an amount equal to the maximum price attained by a
security over a specific time period, discounted for the option’s age. The Russian
option was proposed by Shepp and Shiryaev. Kramkov and Shiryaev first examined
the option in the binomial model. We improve upon their results and give a nearoptimal
algorithm for price determination.
Specifically, we prove that the optimal exercising boundary is monotonic and
give an O(N) dynamic programming algorithm to construct the boundary, where
N is the option expiration time. The algorithm also computes the option’s value at
time zero in time O(N) and the value at all of the O(N3) nodes in the binomial
model in time O(N2).
Keywords: Russian option, binomial model, dynamic programming.
1 Introduction
The Russian Option is a two-party contract which creates a liability for the option
seller to pay the option buyer an amount equal to the maximum price attained
by a security over a specific time period, discounted for the option’s age. For an
N + 1 step time period 0, 1, 2, . . .,N, the option seller’s liability at time step n,
0 ≤ n ≤ N, is,
L(n) = βn max
0≤t≤n
st
Keywords
Russian option, binomial model, dynamic programming.
Related Book
Other papers in this volume
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