Abstract
Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity. In this paper, we consider some type of game options and obtain explicit expressions through solving Stefan(free boundary) problems under condition that the stock price is driven by some jump-diffusion process. Finally, we give a simple application about convertible bonds.
Highlights
Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity
Let Ω, F, P be a probability space hosting a Brownian motion W {Wt : t ≥ 0} and an independent Poisson process N {Nt : t ≥ 0} with the constant arrival rate λ, both adapted to some filtration F {Ft}t≥0 satisfying usual conditions
Note that the absolute value of relative jump sizes is equal to y0, and jumps are downwards. It can be comprehended as a downward tendency of the risky asset price brought by bad news or default and so on
Summary
Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity.
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