We present three models of stock price with time-dependent interest rate, dividend yield, and volatility, respectively, that allow for explicit forms the optimal exercise boundary finite maturity American put option. The satisfies nonlinear integral equation Volterra type. choose parameters model so can be solved in closed form. also define contracts type strike support boundary.

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

When …rms access unbounded liability exposures and are granted limited liability, then an all equity …rm holds a call option, whereby it receives a free option to put losses back to the taxpayers. We call this option the taxpayer put, where the strike is the negative of the level of reserve capital at stake in the …rm. We contribute by (i) valuing this taxpayer put, and (ii) determining the lev...

An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the...