Abstract:
Emerging markets are on the edge of introducing derivative products; however, they are
unable to calibrate and select from the models that are available in the literature due to the
absence of real market derivative prices. The Black and Scholes (BS) model is the sole
pricing model that is sufficient for pricing options based on stock index volatility. This is
due to the fact that the sophistication of other models necessitates the calibration of
additional parameters, which can only converge to true values when calibrated with options
data. Moreover, a good part of mispricing under BS model can be addressed when volatility
updated with time series information under risk neutral dynamics is used as a proxy to BS’s
constant volatility calibrated from cross section of stock market information. Delta-hedged
profit-loss distribution of hypothetical European derivatives without requiring real market
option data under Proxy-BS pricing with several proxies from recent GARCH option
pricing literature such as GARCH, NGARCH, GARCH Jump, GARCH Jumps Constant
can provide information to emerging markets regarding which Proxy-BS model to use for
derivative pricing; at least until real market option data , on developing indices, become
available to calibrate and use more sophisticated option pricing model. Such delta-hedged
profit-loss distribution can help emerging markets infer the Value-at-Risk and Expected
Shortfall for any proxy choice. Then, for the sake of studying the relative riskiness of their
chosen proxy-BS model, it can be replicated for number of developed country's indices
such as S&P500 markets for which real option data are available. Ultimate goal of this
research is to make proposals, with empirical evidence from developed countries derivative
markets, regarding which developing country should follow what dynamic proxy for initial
pricing of their derivative contracts in the absence of real market derivative contract data
on their own indices.
