Abstract
Abstract We develop a novel pricing strategy that approximates the value of an American option with exotic features through a portfolio of European options with different maturities. Among our findings, we show that: (i) our model is numerically robust in pricing plain vanilla American options; (ii) the model matches observed bids and premiums of multidimensional options that integrate ratchet, Asian, and barrier characteristics; and (iii) our closed-form approximation allows for an analytical solution of the option’s greeks, which characterize the sensitivity to various risk factors. Finally, compared to the traditional Monte Carlo simulations method, we highlight that our estimation’s prediction is more accurate and requires less than 1% of the computational time.
Highlights
It has become an empirical regularity that central banks, especially those in emerging countries, frequently intervene in the foreign exchange (FX) markets in order to smooth short-run fluctuations, soothe the fear of floating, build-up international reserves, or even defend a particular target
6In call and put options the aggregate notional amount of the Weighted Time Value (WTV) portfolio needed to minimize the sum of squared residuals between its price and the American option price are m = 1.0179 and m = 1.0305, respectively. 7Particularly we look at the WTV given by: i) a linear weighting of the time value; ii) a simple average of the value of the options in the portfolio; iii) the value given by allocating all the weight to the European option with the greatest time value; and iv) the value given by the allocation of weights according to the formula exp(2tvi)/ ∑Ni=1 exp(2tvi)
Looking at the predicted value of these options, we find that the prediction of the Least Squares Monte Carlo (LSM) algorithm fall in the range of the minimum and maximum observed bids 63% of the time, while our stochastic model based on the WTV methodology falls within the same range in 66% of the auctions (Figures 19 and 20)
Summary
It has become an empirical regularity that central banks, especially those in emerging countries, frequently intervene in the foreign exchange (FX) markets in order to smooth short-run fluctuations, soothe the fear of floating, build-up international reserves, or even defend a particular target (see Calvo and Reinhart 2002; Edwards 2011; and Levy-Yeyati et al 2013). Our empirical pricing model for these options departs from the standard Monte Carlo simulation techniques for studying American options due to the problems that this methodology encounters, namely the proportion of periods for which it yields a price of 0, the absolute unawareness of the possible exercise in intermediate periods, and the computational effort that would make unworkable the study of the behavior of these instruments with the high frequency data that we have for the FX market This allows us to propose a novel valuation strategy in which we approximate the value of an exotic American option through a portfolio of exotic European options.
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