This note defines the premium of a put option on the firm as a measure of insolvency risk. The put premium is not a coherent risk measure as defined by Artzner et al. (1999). It satisfies all the axioms for a coherent risk measure except one, the translation invariance axiom. However, it satisfies a weakened version of the translation invariance axiom that we label translation monotonicity. The...

In this paper, Black Scholes’s pricing model was developed to study American option on future contracts of Brent oil. The practical tests of the model show that market priced option contracts as future contracts less than what model did, which mostly represent option contracts with price rather than without price. Moreover, it suggests call option rather than put option. Using t hypothesis test...

This paper considers the rising price and shrinking demand caused by inflation. To manage these above risks, firm has a chance to place two types of orders in each period, viz., order put options order. formulates multiperiod ordering model, either without or with option contracts. Based on stochastic dynamic programming, this studies optimal policy structure period provides an approximation ev...

The Black-Scholes equations have been increasingly popular over the last three decades since they provide more practical information for optional behaviours. Therefore, effective methods needed to analyze these models. This study will focus mainly on investigating behavior of equation European put option pricing model. To achieve this, numerical solutions model are produced by combined methods....

We study the Option pricing with linear investment strategy based on discrete time trading of underlying security, which unlike existing continuous models provides a feasible real market implementation. Closed form formulas for Call and Put price are established fixed interest rates their extensions to stochastic Vasicek Hull-White rates.