D. Bates. Jumps and stochastic volatility: exchange rate processes implicit in Deutsch mark options. Review of financial studies 9 (1996), 69--107.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....analytically. 1 Introduction The Black Scholes model and its extensions comprise one of the major developments in modern nance. Much of the recent literature on option valuation has successfully applied Fourier analysis to determine option prices, e.g. Bakshi and Chen [1] Scott [13] Bates [5], Heston [8] and Chen and Scott [6] These authors numerically solve for the delta and for the risk neutral probability of nishing in the money, which can be easily combined with the stock price and the strike price to generate the option value. Unfortunately, this approach is unable to harness ....

.... proposed in Geman, Yor, and Madan [7] Characteristic functions have also been used in the pure diusion context with stochastic volatility (Heston [8] and with stochastic interest rates in Bakshi and Chen [1] Finally, they have been used for jumps coupled with stochastic volatility (Bates [5]) and for jumps coupled with stochastic interst rates and volatility in Scott [13] The solution methods can also be applied to average rate claims and to other exotic claims (Bakshi and Madan [2] The methods are generally much faster than nite dierence solutions to partial dierential equations ....

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Bates, David (1996), \Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutschemark Options," Review of Financial Studies, 9, 69-108.

....volatilities vary for di erent strikes and maturities, by producing the so called volatility skew or smile. On the contrary, a suitable choice of the parameters of the jump process can allow to t the model to the observed volatility. For some recent works concerning jump di usion models see [1, 7, 12, 21, 27]. Another recent domain of interest is the analytical modeling framework for jumps in xed income markets, 8, 14, 15, 18, 19, 21, 33] More direct numerical issues are considered in [6] and in the book by D. Tavella and C. Randall [34] From a mathematical side, the problem of existence and ....

D. Bates. Jumps and stochastic volatility: exchange rate processes implicit in Deutsch mark options. Review of nancial studies, 9 (1996), 69-107.

....involve some basis risk when the market participant is no longer certain regarding the present or future value of portfolios. Considerations of profit and loss can be sometimes suppressed by adjusting prices and implied volatilities. Pricing derivatives with stochastic rates and volatilities [2 4] , transaction costs [5,6] hedging constraints [7 8] and other realistic features lead to a designated price increase or decrease. It is supposed to compensate the financial institution for the residual basis risk. As discussed below, it is practically impossible to eliminate the residual ....

D.S. Bates, Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options, The Review of Financial Studies 9 (1996) 69-107.

.... the local volatility surface by Derman and Kani [14] and Dupire [15] Jumps or discontinuities when considered, have been added on as an additional orthogonal compound Poisson process also impacting the stock as for example in Press[38] Merton [34] Cox and Ross [11] Naik and Lee [37] Bates [6], and Bakshi and Chen [1] This class of models is broadly referred to as jump diusion models and as the name suggests they are mixture models studying the high activity and low activity events by using two orthogonal modeling strategies. ....

Bates, D. (1996), \Jumps and Stochastic Volatility: Exchange Rate Processes implicit in Deutschemark Options," The Review of Financial Studies, 9, 69-108.

....(1989) Melino and Thornbull (1990) Stein and Stein (1991) and Amin and Ng (1993) among others. 2 ity as well as prices using the class of jump in volatility models proposed by Du#e, Pan, and Singleton (2000) The DPS class of models generalizes the models in Merton (1976) Heston (1993) and Bates (1996). The results in EJP show that the jump in volatility models provide a significantly better fit to the returns data. EJP also provide decompositions of various large market movements which suggest that large returns, including the crash of 87, are largely explained ex post by a jump to ....

....the di#usion term in the volatility process, is too high to be consistent with time series estimates of the volatility process. The empirical findings reported in this paper can be summarized as follows. Parameter estimates obtained for the (Heston) stochastic volatility model as well as the (Bates (1996)) jump di#usion with jumps in prices, are similar to those in Baksi, Cao, and Chen (1997) In particular, our estimates imply a jump every other year on average, which compared to estimates in EJP from returns data alone, is very low. The volatility of volatility estimates are higher than those ....

Bates, D. (1996). Jump and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options. Review of Financial Studies, 9, 69--107.

....has been grounded in the perspectives of a two asset economy. Initially, this was a harmless assumption as the economy studied was complete and pricing was at the cost of replication. Increasingly it is now recognized that with stochastic volatility and jumps constituting an essential (Bates, [2], Bakshi, Cao and Chen [1] if not indispensible (Carr, Geman, Madan, and Yor [6] part of the stock price dynamics, pricing must be founded on principles other than the cost of replication. The most general of these principles developed in the finance literature is the absence of arbitrage, due ....

Bates, D. (1996), "Jumps and stochastic volatility: Exchange rate processes implicit in deutschemark options," Review of Financial Studies, 9, 69-108.

....the parameters of the stochastic volatility process from observed option prices. The implied variance process of the dollar mark rate exhibits mean reverting, and there is a negative correlation between the spot return and variance process, which suggests a skewed distribution of the spot return. Bates (1996) finds that implied parameter estimates on pooled dollar mark futures options over 19881991 indicating overall a leptokurtic, symmetric distribution. In addition, this approach of estimating the instantaneous implied volatility of the underlying asset return is analogous to the implied binomial ....

....the probability process. Since the currency options traded on PHLX are American style options, it is important to adjust for the early exercise premium. This is done by using the Barone Adesi and Whaley (1987) quadratic approximation method. The performance of this approach has been examined by Bates (1996) and Knoch (1992) 2.2 Data Description Trading records for foreign currency options are taken from the Foreign Currency Options Pricing History database of the Philadelphia Stock Exchange (PHLX) The database contains prices for options on Deutsche mark, Japanese yen, British pound, Swiss ....

Bates, D., (1996),"Jumps and Stochastic Volatility: Exchange Rate Process Implicit in PHLX Foreign Currency Options," Review of Financial Studies, 9, 69-107.

.... [Jacquier, Polson, and Rossi (1994) and Kim, Shephard, and Chib (1998) and simulated method of moments [Due and Singleton (1993) and Andersen and Sorensen (1994,1997) Alternatively, the parameters of stochastic volatility models can be inferred from the cross section of option prices [Bates (1996) and Bakshi, Cao, and Chen (1997) as well as from both option prices and returns on the underlying security [Chernov and Ghysels (2000) Jones (2000) and Pan (2000) 4 There is an analogous class of so called no arbitrage term structure models that are calibrated to t exactly the observed ....

Bates, David S., 1996, Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options, Review of Financial Studies 9, 69-107.

....of models which have analytic characteristic functions for the underlying asset prices or market rates. This includes the Variance Gamma (VG) model [15] the inverse Gaussian model [3] and numerous stochastic volatility and stochastic interest rates models in the general a#ne jump di#usion family [1, 4, 6, 14, 21]. The method extends the fast Fourier transform approach of Carr Madan [5] to a multi factor setting, and is applicable to options with a payo# more complex than a piecewise linear structure. The main idea is to integrate the option payo# over approximate regions bounding the non trivial ....

Bates, D. (1996). Jumps and stochastic volatility: Exchange rate process implicit in Deutschemark options. Review of Financial Studies 9 69--108.

....consistent with observed (or fitted) option prices. Derman and Kani (1994) construct implied binomial trees from an observed volatility smile which is useful for pricing and hedging both standard and exotic options. Following the work of Stein and Stein (1991) Heston (1993) or more recently, Bates (1996), it is possible to link a nonstandard risk neutral density to a rather flexible process driving the evolution of the underlying asset, allowing for possible jumps, stochastic volatility and correlations between the asset price and volatility. In all of these approaches the informational content ....

Bates, D., 1996, "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options." Review of Financial Studies, vol 9, No 1, 69-107.

....prior lognormal density among 4 PETER CARR, H ELYETTE GEMAN, AND DILIP B. MADAN those consistent with observed option prices. Similarly, Buchen and Kelly[12] Stutzer [36] and Avellaneda et al. 3] minimize cross entropy relative to a prior. Alternatively, Hull and White [28] Heston [25] Bates [5], and Madan, Carr, and Chang [30] all specify a tractable and flexible family of risk neutral processes and then estimate parameters from option prices. Ait Sahalia and Lo [1] take a nonparametric approach to the same problem. In all of these papers, the relevance of the selected density remains ....

Bates, D., 1996, "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutschemark Options," Review of Financial Studies, 9, 69-108.

....option pricing models is carried out by Bakshi, Cao, and Chen (1997) They are able to derive a closed form jump diffusion model that includes previously studied models. It allows not only stochastic volatility, but also stochastic interest rates and stochastic jumps. Moreover, following Bates (1996), they use a cross sectional framework to implement their model, and analyze the performance and hedging behavior of the nested option pricing models. Das and Sundaram (1998) also examine the extent to which these models are able to capture the observed anomalies discussed in literature. Bakshi, ....

....therefore introduce the explicit exogenous market price of volatility risk. We face similar problems if we introduce any other non traded source of risks such as systematic jumps or transaction costs. Recent theoretical advances in this literature include Stein and Stein (1991) Heston (1993) and Bates (1996). In particular, Heston (1993) shows that a closed form solution for a European call can be derived as an integral of the future security price density, which itself may be calculated by an inverse Fourier transform. This method may also be applied when correlation between the increments of the ....

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Bates, D. (1996). "Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options", Review of Financial Studies 9, pp. 69-107.

.... volatility of the underlying stock, the observed changes in interest rates or the difference between the observed and the assumed stock price path (like the jump processes) Merton [1976] Hull and White [1987] Scott [1987] Wiggins [1987] Johnson and Shanno [1987] Stein and Stein [1991] Bates [1996], Bakshi and Chen [1997] Cox [1996] Corrado and Su [1996] Madan, Carr and Chan [1998] are examples of models where the basic Black Scholes assumptions are dropped. Some other authors impute the smile to the behaviour of traders or to their risk aversion, such in Bookstaber [1991] Grossman and ....

BATES, D. (1996), "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in PHLX Deutschemark Options", Review of Financial Studies, 9, pp. 69-107.

....the e#ect on international portfolio choice of the following two stylized facts about returns on international equities. One, returns are characterized by jumps leading to distributions that are skewed and have fat tails, as documented by, for example, Jorion (1988) Akgiray and Booth (1988) Bates (1996), and Bekaert, Erb, Harvey and Viskanta (1998) Two, these jumps in returns tend to occur at the same time across equities in di#erent countries, for which a variety of explanations have been o#ered by Engle, Ito and Lin (1990) King and Wadhwani (1990) and Harvey and Huang (1991) 1 One ....

Bates, David. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, 1996, v9(1), 69-107.

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D. Bates. Jumps and stochastic volatility: exchange rate processes implicit in Deutsch mark options. Review of financial studies 9 (1996), 69--107.

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D. Bates, Jumps and stochastic volatility: the exchange rate processes implicit in Deutschemark options, Rev. Fin. Studies, 9 (1996), pp. 69--107.

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Bates, D. (1996), \Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutschemark Options," Review of Financial Studies, 9, 69-108.

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Bates, D. S. (1996), "Jumps and Stochastic Volatility: Exchange Rate Process Implicit in Deutsche Mark Options," Review of Financial Studies, 9, 1, 69-107.

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Bates, David (1996), "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutschemark Options," Review of Financial Studies, 9, 69-108.

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Bates, D. (1996a): Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options, Review of Financial Studies, 9, 69-107.

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Bates, D. (1996a), \Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, 9, 69-107.

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Bates, D. S. (1996), Jumps and Stochastic Volatility: Exchange Rate Process Implicit in Deutsche Mark Options, Review of Financial Studies 9, 69-107.

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David Bates. Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. Review of Financial Studies, 9:69--107, 1996b.

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Bates, D.S.(1996): "Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options," Review of Financial Studies 9, 69-107.

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Bates, D.S.(1996): "Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options," Review of Financial Studies 9, 69-107.

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