Pricing Options Under Conservative Conditions

Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount have found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract for the underlying asset follows a geometric Brownian motion with constant interest rate, volatility and nonnegative dividend yield. In this paper, option price is derived for the case of the underlying asset that follows a geometric Brownian motion with time-dependent drift and volatility, which is more important for real life applications. The option price formulae are derived for the case of a drift that includes nonnegative or negative dividend. The latter yields a solution type that is new to the literature. A negative dividend corresponds to a negative foreign interest rate for foreign exchange options, or storage costs for commodity options. It may also appear in pricing options with transaction costs or real options, where the drift is larger than the interest rate.

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Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging

Quantitative Finance ◽

10.1080/14697688.2013.816766 ◽

2013 ◽

Vol 14 (3) ◽

pp. 427-442 ◽

Cited By ~ 3

Author(s):

Igor Halperin ◽

Andrey Itkin

Keyword(s):

Static Hedging ◽

Pricing Options ◽

Utility Indifference ◽

Illiquid Assets

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Volatility Forecast by Volatility Index and Its Use as a Risk Management Tool Under a Value-at-Risk Approach

Review of Pacific Basin Financial Markets and Policies ◽

10.1142/s0219091518500108 ◽

2018 ◽

Vol 21 (02) ◽

pp. 1850010 ◽

Cited By ~ 3

Author(s):

Yam Wing Siu

Keyword(s):

At Risk ◽

Risk Management ◽

Risk Premium ◽

Value At Risk ◽

Realized Volatility ◽

Management Tool ◽

Spot Price ◽

Pricing Options ◽

Significance Levels ◽

Risk Approach

This paper examines the predicting power of the volatility indexes of VIX and VHSI on the future volatilities (or called realized volatility, [Formula: see text] of their respective underlying indexes of S&P500 Index, SPX and Hang Seng Index, HSI. It is found that volatilities indexes of VIX and VHSI, on average, are numerically greater than the realized volatilities of SPX and HSI, respectively. Further analysis indicates that realized volatility, if used for pricing options, would, on some occasions, result in greatest losses of 2.21% and 1.91% of the spot price of SPX and HSI, respectively while the greatest profits are 2.56% and 2.93% of the spot price of SPX and HSI, respectively, making it not an ideal benchmark for validating volatility forecasting techniques in relation to option pricing. Hence, a new benchmark (fair volatility, [Formula: see text] that considers the premium of option and the cost of dynamic hedging the position is proposed accordingly. It reveals that, on average, options priced by volatility indexes contain a risk premium demanded by the option sellers. However, the options could, on some occasions, result in greatest losses of 4.85% and 3.60% of the spot price of SPX and HSI, respectively while the greatest profits are 4.60% and 5.49% of the spot price of SPX and HSI, respectively. Nevertheless, it can still be a valuable tool for risk management. [Formula: see text]-values of various significance levels for value-at-risk and conditional value-at-value have been statistically determined for US, Hong Kong, Australia, India, Japan and Korea markets.

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