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The arbitrage inconsistencies of implied volatility extraction in connection to calendar bandwidth
Vitali, Sebastiano ; Tichý, Tomáš ; Kopa, Miloš
Options are often priced by Black and Scholes model by using artificial (and unobserved) volatility implied by option market prices. Since many options do not have their traded counterparts with the same maturity and moneyness, it is often needed to interpolate the volatility values. The general procedure of implied volatility extraction from market prices and subsequent smoothing can, however, lead to inconsistent values or even arbitrage opportunities. In this paper, a potential arbitrage area is studied in connection with the calendar bandwidth construction.
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The Bandwidth Selection in Connection to Option Implied Volatility Extraction
Tichý, T. ; Kopa, Miloš ; Vitali, S.
Among various kinds of options we can found at the market, some are traded at organized exchanges and therefore are quite liquid, while others are traded only between particular parties. Whereas there is no need to look for a model to price liquid exchange traded options, since their price is generally accepted by the demand and supply, for illiquid or even exotic options new efficient models are still developed. The current market practice is to obtain the implied volatility of liquid options as based on Black-Scholes type (BS hereafter) models. The focus of this paper is to study the behavior of IV and SPD for several kernel functions and with respect to different choices of bandwidth parameter h. Specifically, we show several interesting implications of the change of h on the violation of no arbitrage condition and the total area of SPD under zero.
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Model of Risk and Losses of a Multigeneration Mortgage Portfolio
Šmíd, Martin
During the last decades, Merton-Vasicek factor model (1987), later generalize by Frye at al. (2000), became standards in credit risk management. We present a generalization of these models allowing multiple sub-portfolios of loans possibly starting at different times and lasting more than one period. We show that, given this model, a one-to-one mapping between factors and the overall default rate and the charge-off rate exists, is differentiable and numerically computable.
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On the pricing of illiquid options with Black-Scholes formula
Tichý, Tomáš ; Kopa, Miloš ; Vitali, S.
Detecting the fair, ie. no-arbitrage, price of an option is a very interesting and challenging task of quantitative finance. It results mostly from the fact that the option payoff is nonlinear and the price can be very sensitive to the changes of underlying factors (especially ATM options). From the other point of view, ATM vanilla options are often traded and liquid, while deep ITM and OTM options are mostly illiquid and it is difficult to estimate the model parameters. Another issue is how to obtain the market assumptions about riskless rate relevant for the option maturity and the future expected dividends. In this paper we focus on a particular problem of extracting parameters to value options on dividend paying stocks via BS model using real data from German option market.
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