Τυχαίες ευκαιρίες βέβαιου κέρδους και επιπτώσεις του στην τιμολόγηση χρηματοοικονομικών παραγώγων
Stochastic arbitrage return and its linchpin with pricing of financial derivatives
In this paper, random arbitrage opportunities and their linchpin with the pricing of financial derivatives will be studied. An unbalanced model will be used so as to set up a stochastic portfolio. As it concerns the random arbitrage return, a rapidly changing in time, stationary ergodic random process will be utilized. As option price and random arbitrage returns are changing on different time scales, an asymptotic pricing theory involving the Central Limit Theorem for random processes will be developed. Our study will be limited to finding pricing bands for options rather than accurate values, which are shown to be independent of the detailed statistical characteristics of the arbitrage returns. In addition, the volatility curve, known as the smile effect, will be shown. “Smile” curve illustrates the implied volatility as a function of the strike price of the option and can be explained in terms of the random arbitrage return. Finally, the stochastic models will be applied by using numerical examples.