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Our derivatives valuation approach as well as interpretation of the notion 'derivatives price' is completely different from BlackScholes benchmark. Black Scholes defined option price as one that can be drawn from their ‘dynamic’ hedging strategy. From financial point of view this strategy can be interpreted as a settlement price between option buyer and a counterparty which finance option buyer at riskfree interest. Note that the notion price of an instrument in Finance always is interpreted as a settlement price between buyer and seller. The second drawback that immediately stems from the buyer – borrower settlement pricing is incorrect randomization. Black and Scholes focusing on spot option price definition ignored the fact of market risk factor of their theoretical option price. They lost the fact that in perfect following their ‘nofreelunch’ strategy either buyer or seller of the option are subject of the market risk. The third drawback of their construction is the mathematical error which was discussed in details in paper ‘Derivatives pricing’ here on slideshare.net.
Our pricing concept is based on sellerbuyer settlement pricing. For each market scenario which uniquely specifies derivative underling price at any moment we define market price of the derivative. For example the market price of a European call option is equal to zero if for the scenario the price of the underlying asset is bellow of the specified strike price. If for the chosen scenario the price of the underlying exceeds the strike price then market price of the option is defined based on the rule which states that interest rate on risky underlying and derivatives must be equal. Thus, when investment in option is meaningful this construction eliminates an arbitrage opportunity for each market scenario. Spot price of the option is a number which can be interpreted as weighted average of the primary market factors such as surplus and demand or risk and reward. Then the value of the market risk of the buyer of the call option is associated with the probability that market price is bellow than spot price while the value of the market risk of the option seller is the adjacent probability. This construction of the market risk can be identify as when spot price is overpriced for option buyer or underpriced for option seller correspondingly. One important conclusion from our definition is the fact that there is no ‘perfect’ price of the option. Any spot price including heuristic BlackScholes’ no arbitrage pricing always implies market risk.