In this short notice, we present structure of the perfect hedging. Closed form formulas clarify the fact that Black-Scholes (BS) portfolio which provides perfect hedge only at initial moment. Holding portfolio over a certain period implies additional cash flow, which could not be imbedded in BS...

In this paper we present a critical point on connections between stock volatility, implied volatility, and local volatility. The essence of the Black Sholes pricing model is based on assumption that option piece is formed by no arbitrage portfolio. Such assumption effects the change of the real...

In this paper, we present somewhat alternative point of view on early exercised American options. The standard valuation of the American options the exercise moment is defined as one, which guarantees the maximum value of the option. We discuss the standard approach in the first two sections of...

In some papers it have been remarked that derivation of the Black Scholes Equation (BSE) contains mathematical ambiguities. In particular there are two problems which can be raise by accepting Black Scholes (BS) pricing concept. One is technical derivation of the BSE and other the pricing...

Regulations of the market require disclosure of information about the nature and extent of risks arising from the trades of the market instruments. There are several significant drawbacks in fixed income pricing modeling. In this paper we interpret a corporate bond price as a random variable. In...

The document IFRS 7 requires disclosure of information about the nature and extent of risks arising from trading those instruments. There are several significant drawbacks in derivative price modeling which relate to global regulations of the derivatives market. Here we present a unified...

In some papers we remarked that derivation of the Black Scholes Equation (BSE) contains mathematical ambiguities. In particular, there are two problems which can be raised by accepting Black Scholes (BS) pricing concept. One is technical derivation of the BSE and the other the pricing definition...

In this paper that is the second part of [1] we outlined basic of foreign exchange and its randomization. We presented a model of forward rate implied by stochastic bond prices. A particular attention is paid to a construction of the LIBOR rate. In our models we distinct stochastic pricing of a...