Related papers: Defaultable perpetual Russian option Under a last …
This paper presents a derivation of the explicit price for the perpetual American put option in the Black-Scholes model, time-capped by the first drawdown epoch beyond a predefined level. We demonstrate that the optimal exercise strategy…
We derive the explicit price of the perpetual American put option cancelled at the last passage time of the underlying above some fixed level. We assume the asset process is governed by a geometric spectrally negative L\'evy process. We…
We study perpetual American option pricing problems in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values of its maximum and maximum drawdown.…
We discuss the pricing of defaultable assets in an incomplete information model where the default time is given by a first hitting time of an unobservable process. We show that in a fairly general Markov setting, the indicator function of…
We study optimal stopping problems related to the pricing of perpetual American options in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values…
We build a general model for pricing defaultable claims. In addition to the usual absence of arbitrage assumption, we assume that one defaultable asset (at least) looses value when the default occurs. We prove that under this assumption, in…
We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black-Scholes equation…
It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper…
We consider the problem of finding the optimal time to sell a stock, subject to a fixed sales cost and an exponential discounting rate \rho. We assume that the price of the stock fluctuates according to the equation dY_t=Y_t(\mu…
We consider a market model where there are two levels of information. The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can…
This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown epoch beyond a predefined level. We consider the market in which an asset price is described by geometric L\'evy…
In this paper we address the problem of optimal liquidation of a large portfolio composed by securities exposed to default risk. The default time is described in terms of a Brownian motion representing the evolution of the value of the…
We study the valuation of an American put option with a random time horizon given by the last exit time of the underlying asset from a fixed level. Since this random time is not a stopping time, the problem falls outside the classical…
We consider a portfolio optimization problem in a defaultable market with finitely-many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market…
We derive closed-form solutions to the optimal stopping problems related to the pricing of perpetual American standard and lookback put and call options in the extensions of the Black-Merton-Scholes model with progressively enlarged…
We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock written on a default-free dividend process,…
Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in…
In this paper we present a MATLAB version of a non-standard finite difference scheme for the numerical solution of the perpetual American put option models of financial markets. These models can be derived from the celebrated Black-Scholes…