caa a22 4500 388047577 CHVBK 20180307125042.0 cr unu---uuuuu 161130e199809 xx s 000 0 eng 10.2307/2331102 doi S0022109000001009 pii (NATIONALLICENCE)cambridge-10.2307/2331102 Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution [Elektronische Daten] Arithmetic Asian options are difficult to price and hedge as they do not have closed-form analytic solutions. The main theoretical reason for this difficulty is that the payoff depends on the finite sum of correlated lognormal variables, which is not lognormal and for which there is no recognizable probability density function. We use elementary techniques to derive the probability density function of the infinite sum of correlated lognormal random variables and show that it is reciprocal gamma distributed, under suitable parameter restrictions. A random variable is reciprocal gamma distributed if its inverse is gamma distributed. We use this result to approximate the finite sum of correlated lognormal variables and then value arithmetic Asian options using the reciprocal gamma distribution as the state-price density function. We thus obtain a closed-form analytic expression for the value of an arithmetic Asian option, where the cumulative density function of the gamma distribution, G(d) in our formula, plays the exact same role as N(d) in the Black-Scholes/Merton formula. In addition to being theoretically justified and exact in the limit, we compare our method against other algorithms in the literature and show our method is quicker, at least as accurate, and, in our opinion, more intuitive and pedagogically appealing than any previously published result, especially when applied to high yielding currency options. Copyright © School of Business Administration, University of Washington 1998 Milevsky Moshe Arye Schulich School of Business, York University, 4700 Keele Street, Ontario, M3J 1P3, Canada Posner Steven E. Marsh & McLennan Securities Corp., Two World Trade Center, New York, NY 10048 Journal of Financial and Quantitative Analysis Cambridge University Press 33/3(1998-09), 409-422 0022-1090 33:3<409 1998 33 JFQ https://doi.org/10.2307/2331102 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2331102 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Milevsky Moshe Arye Schulich School of Business, York University, 4700 Keele Street, Ontario, M3J 1P3, Canada NATIONALLICENCE 700 1- Posner Steven E. Marsh & McLennan Securities Corp., Two World Trade Center, New York, NY 10048 NATIONALLICENCE 773 0- Journal of Financial and Quantitative Analysis Cambridge University Press 33/3(1998-09), 409-422 0022-1090 33:3<409 1998 33 JFQ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge