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35
A closedform solution for options with stochastic volatility with applications to bond and currency options
 Review of Financial Studies
, 1993
"... I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond option ..."
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Cited by 1512 (6 self)
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I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strikeprice biases in the BlackScholes (1973) model. The solution technique is based on characteristic functions and can be applied to other problems. Many plaudits have been aptly used to describe Black and Scholes ’ (1973) contribution to option pricing theory. Despite subsequent development of option theory, the original BlackScholes formula for a European call option remains the most successful and widely used application. This formula is particularly useful because it relates the distribution of spot returns I thank Hans Knoch for computational assistance. I am grateful for the suggestions of Hyeng Keun (the referee) and for comments by participants
An Analysis of Secured Debt
 Journal of Financial Economics
, 1985
"... This paper analyzes the pricing of two types of secured debt and shows that secured debt can be used to increase the value of the firm. In particular, it is shown that some profitable projects will not be undertaken by a firm which can use only equity or unsecured debt to finance them but will be un ..."
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Cited by 124 (1 self)
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This paper analyzes the pricing of two types of secured debt and shows that secured debt can be used to increase the value of the firm. In particular, it is shown that some profitable projects will not be undertaken by a firm which can use only equity or unsecured debt to finance them but will be undertaken if they can be financed with secured debt. Secured debt is priced for a firm with two assets and some unsecured debt outstanding. The pricing results are used to illustrate the benefits of the security provision of secured debt. 1.
A GARCH Option Pricing Model with Filtered Historical Simulation
 Review of Financial Studies
, 2008
"... We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model’s flexibility to fit market option prices. An extensive ..."
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Cited by 29 (3 self)
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We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model’s flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 Index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black–Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility, and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.
Stochastic volatility: option pricing using a multinomial recombining tree
, 2006
"... We treat the problem of option pricing under the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be meanreverting. Assuming that only discrete past stock information is available, we adapt an interacting ..."
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Cited by 17 (5 self)
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We treat the problem of option pricing under the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be meanreverting. Assuming that only discrete past stock information is available, we adapt an interacting particle stochastic filtering algorithm due to Del Moral, Jacod and Protter (Del Moral et al., 2001) to estimate the SV, and construct a quadrinomial tree which samples volatilities from the SV filter’s empirical measure approximation at time 0. Proofs of convergence of the tree to continuoustime SV models are provided. Classical arbitragefree option pricing is performed on the tree, and provides answers that are close to market prices of options on the SP500 or on bluechip stocks. We compare our results to nonrandom volatility models, and to models which continue to estimate volatility after time 0. We show precisely how to calibrate our incomplete market, choosing a specific martingale measure, by using a benchmark option. Key words and phrases: incomplete markets, MonteCarlo method, options market, option pricing, particle method, random tree, stochastic filtering, stochastic volatility. 1
Estimation and Pricing under LongMemory Stochastic Volatility
"... We treat the problem of option pricing under a stochastic volatility model that exhibits longrange dependence. We model the price process as a Geometric Brownian Motion with volatility evolving as a fractional OrnsteinUhlenbeck process. We assume that the model has longmemory, thus the memory par ..."
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Cited by 8 (3 self)
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We treat the problem of option pricing under a stochastic volatility model that exhibits longrange dependence. We model the price process as a Geometric Brownian Motion with volatility evolving as a fractional OrnsteinUhlenbeck process. We assume that the model has longmemory, thus the memory parameter H in the volatility is greater than 0.5. Although the price process evolves in continuous time, the reality is that observations can only be collected in discrete time. Using historical stock price information we adapt an interacting particle stochastic filtering algorithm to estimate the stochastic volatility empirical distribution. In order to deal with the pricing problem we construct a multinomial recombining tree using sampled values of the volatility from the stochastic volatility empirical measure. Moreover, we describe how to estimate the parameters of our model, including the longmemory parameter of the fractional Brownian motion that drives the volatility process using an implied method. Finally, we compute option prices on the S&P 500 index and we compare our estimated prices with the market option prices.
STOCK MARKET VOLATILITY AND THE FORECASTING ACCURACY OF IMPLIED VOLATILITY INDICES
, 2006
"... Nabil MAGHREBI* ..."
Pricing and Hedging Strategy for Options with Default and Liquidity Risk
, 2010
"... This study applies fuzzy set theory to the vulnerable BlackScholes (1973) or Merton (1973) formula. Expectations of heterogeneity mean option prices are expected to be imprecise, thus making it natural to consider fuzziness to handle this. This article presents a fuzzy approach to value BlackSchol ..."
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This study applies fuzzy set theory to the vulnerable BlackScholes (1973) or Merton (1973) formula. Expectations of heterogeneity mean option prices are expected to be imprecise, thus making it natural to consider fuzziness to handle this. This article presents a fuzzy approach to value BlackScholes options subject to nonidentical rationality and correlated credit risk. Although no analytical solution is available, this study employs a fuzzy approach to derive an approximate analytical expression for the upper and lower bounds of the European fuzzy vulnerable option price. Furthermore, the Greeks and hedging strategy of the proposed model are also provided in this article.
Working paper series WP FIECAC 13.01 Evaluating the effects of the EU directive proposal for risk based deposit insurance premiums in Spain DEPARTMENT OF FINANCIAL ECONOMICS AND ACCOUNTING 2 EVALUATING THE EFFECTS OF THE EU DIRECTIVE PROPOSAL FOR RISKBA
"... Abstract This paper analyzes the effects on the Spanish banking system of the EU proposal for a new Directive on deposit insurance systems based on risksensitive premiums. To do this, we examine the risk profile of Spanish banks during the 20072011 period according to several indicators reflectin ..."
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Abstract This paper analyzes the effects on the Spanish banking system of the EU proposal for a new Directive on deposit insurance systems based on risksensitive premiums. To do this, we examine the risk profile of Spanish banks during the 20072011 period according to several indicators reflecting capital adequacy, asset quality, profitability and liquidity. We conclude that most of banks would increase their contributions with the proposed system, evidencing the cyclical character of the new model. Our results also suggest that riskbased schemes could provide an incentive for sound management by reducing the premiums for those banks with better risk profiles. JEL classification: G21; G22; G28
Center for Economic Institutions
, 2004
"... We propose a new method to compute option prices based on GARCH models. In an incomplete market framework, we allow for the volatility of asset return to differ from the volatility of the pricing process and obtain adequate pricing results. We investigate the pricing performance of this approach ove ..."
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We propose a new method to compute option prices based on GARCH models. In an incomplete market framework, we allow for the volatility of asset return to differ from the volatility of the pricing process and obtain adequate pricing results. We investigate the pricing performance of this approach over short and long time horizons by calibrating theoretical option prices under the Asymmetric GARCH model on S&P 500 market option prices. A new simplified scheme for delta hedging is proposed. 2