Archive
Black’s brilliant model was originally developed for pricing European futures options (“The Pricing of Commodity Contracts,” Journal of Financial Economics, 3 (March 1976)). Later, it turned out to […]
A futures option is the right, but not the obligation, to enter into a futures transaction at a predetermined futures price, by a predetermined date. The final date […]
Why diversification fails during market crises… Assume two variables, (x_1) and (x_2), follow generalized Wiener processes: dx1 = a1·dt + b1·dz1 and dx2 = a2·dt + b2·dz2 The […]
To describe the evolution of a derivative of stock price, we use Ito’s Lemma. For example, through it we can express the fair forward price of a stock […]
Without the discoveries of the Japanese mathematician Kiyoshi Itô (伊藤 清, 1915–2008), the Black–Scholes–Merton model — and therefore the modern derivatives market — could not exist. Before moving […]
If physicists use the Wiener process to describe the movement of molecules, for finance it is interesting because it helps us understand the price behavior of stocks and […]
Why is uncertainty considered proportional to the square root of time (√t)? A Markov process (named after the Russian mathematician Andrey Markov (1856–1922)) is a special case of […]
