The least-squares Monte Carlo method of Longstaff-Schwartz is utilized to construct the optimal exercise boundary (OXB) of an American put option when the underlying follows a geometric Brownian motion (GBM). The optimal exercise price at each time step is obtained by solving numerically the...

The pricing accuracy of the canonical least-squares Monte Carlo (CLM) method can be improved significantly by incorporating innovatively a variance constraint in the derivation of the canonical risk-neutral distribution. This new approach is called the variance-constrained CLM (vCLM) in the...

The pricing formulas for European call and put options under arithmetic Brownian motion (ABM) are derived via risk-neutral valuation using the martingale measure, and checked against the corresponding Black-Scholes-like partial differential equation (PDE). In quite a few limiting cases, the...

Options pricing and hedging under canonical valuation have recently been demonstrated to be quite effective, but unfortunately are only applicable to European options. In this paper, a variation of canonical valuation called canonical least-squares Monte Carlo is proposed to price American...

Warrants on China's A-share market exhibited prolonged abnormal patterns by trading significantly below their intrinsic values. One might simply deem this phenomenon as uninteresting by pointing out that the A-share market is incomplete, for short selling of stocks is prohibited. This reasoning...

A convertible bond (CB) with a right of m out of n day provisional call or soft-call becomes callable given that the underlying stock closes above a pre-set trigger price for any m or more days over the n consecutive trading days up to the current day. It is computationally challenge to value...

In his 2009 Letter to Investors, Buffett discussed in some details about the problems of the Black-Scholes formula when applied to extremely long-dated put options. This short comment shows that if his arguments are interpreted in the usual way, he probably made several mistakes in his Letter....

Surface evaporation is one of the main processes in the soil–atmosphere interaction. Since it is highly related to meteorological factors and soil properties, determination of evaporation rate from soil surface remains a challenge. To investigate the evaporation from unsaturated soil, a...