In the current paper, we develop a methodology to price lookback options for cryptocurrencies. We propose a discretely monitored window average lookback option, whose monitoring frequencies are randomly selected within the time to maturity, and whose monitoring price is the average asset price...

In 2009, Avellaneda and Lipkin (A&L) proposed a dynamic model for hard-to-borrow stocks, in which the stock price and the buy-in rate, an additional factor introduced by them, are full coupled. In order to obtain a semi-explicit pricing formula for European call options, A&L had to make an...

The behavior of the optimal exercise price of American puts near expiry has been well studied under the Black-Scholes model as a result of a series of publications. However, the behavior of the optimal exercise price under a stochastic volatility model, such as the Heston model, has not been...