In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black-Scholes models. We analyze European, Asian, American, Parisian and perpetual options and conclude that the...

This paper presents a comprehensive extension of pricing two-dimensional derivatives depending on two barrier constraints. We assume randomness on the covariance matrix as a way of generalizing. We analyse common barrier derivatives, enabling us to study parameter uncertainty and the risk...

It is generally said that out-of-the-money call options are expensive and one can ask the question from which moneyness level this is the case. Expensive actually means that the price one pays for the option is more than the discounted average payoff one receives. If so, the option bears a...

Astonishingly little attention has been paid in academic literature to the 2008-2009 foreign exchange (FX) options debacle in Poland, the scale of which was unheard of. It affected not only an individual organization but a significant part of economy, being an example of a situation in which...

I document a sizeable bias that might arise when valuing out of the money American options via the Least Square Method proposed by Longstaff and Schwartz (2001). The key point of this algorithm is the regression-based estimate of the continuation value of an American option. If this regression...

The paper deals with defaultable markets, one of the main research areas of mathematical finance. It proposes a new approach to the theory of such markets using techniques from the calculus of optional stochastic processes on unusual probability spaces, which was not presented before. The paper...

Trading in binary options is discussed using an approach based on expected profit (EP) and expected loss (EL) as metrics of reward and risk of trades. These metrics are reviewed and the role of the EL/EP ratio as an indicator of quality of trades, taking risk tolerance into account, is...

When trading in the call and put contracts of option chains, the portfolios of strikes must be selected. The trader must also decide whether to take long or short positions at the selected strikes. Dynamic strategies for making these decisions are discussed in this paper. On any day, the...

This paper considers risks of the investment portfolio, which consist of distributed mortgages and sold European call options. It is assumed that the stream of the credit payments could fall by a jump. The time of the jump is modeled by the exponential distribution. We suggest that the returns...

In this paper, we focus on an implicit assumption in the BSM framework that limits the scope of market network connections to seeking gains in the currency basis, i.e., on trading strategies between the numeraire and the stock and between the numeraire and the option, separately. We relax this...