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Valuation of portfolios under uncertain volatility : Black-Scholes-Barenblatt equations and the static hedging

<p>The famous Black-Scholes (BS) model used in the option pricing theory</p><p>contains two parameters - a volatility and an interest rate. Both</p><p>parameters should be determined before the price evaluation procedure</p><p>starts. Usually one use the historical data to guess the value of these</p><p>parameters. For short lifetime options the interest rate can be estimated</p><p>in proper way, but the volatility estimation is, as well in this case,</p><p>more demanding. It turns out that the volatility should be considered</p><p>as a function of the asset prices and time to make the valuation self</p><p>consistent. One of the approaches to this problem is the method of</p><p>uncertain volatility and the static hedging. In this case the envelopes</p><p>for the maximal and minimal estimated option price will be introduced.</p><p>The envelopes will be described by the Black - Scholes - Barenblatt</p><p>(BSB) equations. The existence of the upper and lower bounds for the</p><p>option price makes it possible to develop the worse and the best cases</p><p>scenario for the given portfolio. These estimations will be financially</p><p>relevant if the upper and lower envelopes lie relatively narrow to each</p><p>other. One of the ideas to converge envelopes to an unknown solution</p><p>is the possibility to introduce an optimal static hedged portfolio.</p>

Identiferoai:union.ndltd.org:UPSALLA/oai:DiVA.org:hh-1634
Date January 2007
CreatorsKolesnichenko, Anna, Shopina, Galina
PublisherHalmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Högskolan i Halmstad/Sektionen för Informationsvetenskap, Data- och Elektroteknik (IDE)
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, text

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