Rationality parameter for exercising American put - Kamille Sofie Tågholt Gad; Jesper Lund Pedersen (Risks, 2015)
In this paper, irrational exercise behavior of the buyer of an American put is characterized by a single parameter. We model irrational exercise rules as the first jump time of a point processes with stochastic intensity. By the rationality parameter, we parameterize a family of stochastic intensities that depends on the value of the put itself. We present a probabilistic proof that the value of the American put using the irrational exercise rule converges to the arbitrage-free price as the rationality parameter converges to infinity. Another application of this result is the penalty method for approximating the price of an American put.
Keywords: 330; behavioral modeling; irrational exercise rule; partial differential equation; penalty method