Follmer H. and Sondermann D., 1986, "Hedging of non-redundant contingent claims".  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and risky strategies to risk less replication of contingent claims. Such investors should be provided with a tool, which enables them to select appropriate hedging strategies and serve their personal risk profiles. Moreover, in incomplete markets risk can only be eliminated at a high cost [9 17] , and probabilistic approach seems to be the most natural one. With this in mind we suggest to consider this risk in detail, and focus on the probability distribution of profit and loss. Pricing in this respect becomes a separate issue, which should only be attempted after the P L distribution ....

H. Fllmer and D. Sondermann, Hedging of Non-redundant Contingent Claims. In W. Hildenbrand and A. Mas-Colell (eds.) Contributions to Mathematical Economics (1986.

....hedge, one can still try to minimize the variance of the lack of hedging under the probability P. Since E i (L K T ) 2 j = 6 E i L K ; L K T j , this amounts to minimizing L K ; L K t for all t 2 [0; T ] This approach has been used in other contexts (see [11] and [1] In order to characterize the process K which minimizes L K ; L K , we need to introduce some notation. The d Thetad matrix A t A t may not be invertible (especially if m d) We will denote by (A t A t ) Gamma1 its pseudo inverse, which is defined by the following : 8J ....

H. Follmer, D. Sondermann, Hedging of Non Redundant Contingent Claims, in Contributions to Mathematical Economics in Honor of Gerard Debreu, W.Hildebrand, A. Mas-Colell eds, North-Holland, Amsterdam, 1986. 24

....and Kulldorff (1999) Another problem being actively investigated is a mean variance hedging, in which EjX(T ) Gamma j 2 is to be minimized, where is a random claim which can not be replicated perfectly. For this problem, an explicit solution was obtained for a very general model (see e.g. Follmer and Sondermann (1986), Duffie and Richardson (1991) Pham et al. (1998) Laurent and Pham (1999) The corresponding optimal hedging strategies are mixture of Merton s strategies and Black Scholes strategies. For all these strategies, the volatility coefficient is assumed to be known, and the strategies depend on the ....

Follmer, H., and Sondermann, D. (1986): Hedging of non-redundant contingent claims. Contributions to Mathematical Economics, A. Mas-Colell and W. Hildenbrand ed. North-Holland, Amsterdam, 205--223.

....changes in aggregate consumption maximizes his expected utility using the LRNVR. The LRNVR incorporates a constant volatility risk premium that is directly linked to the risk premium in the mean. The alternative concept of minimizing the quadratic loss of a hedge portfolio, as pioneered by Follmer and Sondermann (1986), will in general lead to a different choice of the pricing measure. The minimal equivalent martingale measure as defined by Follmer and Schweizer (1991) is, intuitively, characterized by the smallest distance (in terms of a relative entropy, i.e. Kullback Leibler distance) to the empirical ....

Follmer, H., Sondermann, D. (1986) Hedging of Non-redundant Contingent Claims, in: Hildenbrand, W., Mas-Colell, A. (eds.), Contributions to Mathematical Economics, Amsterdam, North Holland, 205--223.

....in a very natural way. See for instance Davis and Robeau (1994) Embrechts and Meister (1995) and references therein. By now a must for all interested in incomplete markets is the so called Fllmer Schweizer Sondermann approach based on the minimisation of expected squared hedge error. See Fllmer and Sondermann (1986), Fllmer and Schweizer (1989) and the interesting discussion by Dybvig (1992) 8 4 Back to insurance At the Bowles Symposium on Securitization of Risk, Georgia State University, Atlanta (1995) Morton Lane (see Lane (1996) brought all of us methodologists back with their feet on the ground by ....

H. Fllmer and D. Sondermann (1986) Hedging of non-redundant contingent claims. In: W. Hildebrand and A. Mas-Collel, (Eds.), Contributions to Mathematical Economics in Honor of Gerard Debreu, Elsevier North--Holland, Amsterdam, pp. 205-223.

.... time T , and U( Delta) is an utility function (see e.g. 5] 8] 9] 10] 15] 17] 19] Another problem being actively investigated is the problem involving a mean variance hedging, i.e. a problem in which EjX(T ) Gamma j 2 is to be minimized, where is a random claim (see e.g. 4] [7], 11] 12] 16] Explicit formulas for optimal strategies for all these optimal investment problems are now available for cases when appreciation rates are random, but can be observed. However, it is practically not possible to accurately estimate the appreciation rates from the real market ....

H. Follmer and D. Sondermann, Hedging of non-redundant contingent claims. In: A. Mas-Colell and W. Hildenbrand (eds). Contributions to Mathematical Economics, North-Holland, Amsterdam, 1986, pp. 205--223.

....We assume that the stock price moves according to a Poisson jump dioeusion process with constant parameters and lognormally distributed jump sizes, as it was rst studied in the context of option valuation by Merton (1976) We particularly focus on the locally risk minimizing hedging strategy. F#llmer and Sondermann (1986) pioneered this approach in the special case where the discounted actual stock price follows a martingale. At each point in time they require that the risk, dened as the expected quadratic hedging error, is minimized. However, in semimartingale models a risk minimizing strategy does not always ....

....we consider Bates (1991) pricing model for systematic jump risk and compare a locally variance minimizing (LVM) strategy and a Delta hedging strategy. 3. 1 Locally Risk Minimizing Hedging Strategy In an incomplete market where the actual discounted stock price process follows a martingale, F#llmer and Sondermann (1986) introduce a mean self nancing, riskminimizing hedging strategy: They dene a risk process R t (OE; j) j E ( Gamma T Gamma Gamma t ) 2 jF t ) representing the expected remaining quadratic hedging error. A strategy is called risk minimizing if it minimizes R t for each t T . It exists in ....

F#llmer, H. and D. Sondermann (1986): Hedging of Non-Redundant Contingent Claims, Contributions to Mathematical Economics, 205-223.

....the hedging error is by considering the variance of this random variable which subsequently is to be minimized. This leads to the well known concept of the variance optimal martingale measure (see [10] and [12, 13] which is closely related to the notion of the minimal martingale measure (see [4] and [3] and gives rise to a hedging strategy using the Galtchouk Kunita Watanabe projection in an appropriate Hilbert space. Following [11, Example 4.3] we explicitly calculate this strategy and the variance of the corresponding hedging error and analyze its asymptotic behavior as the ....

H. Follmer and D. Sondermann, Hedging of non-redundant contingent claims, in: Contributions to Mathematical Economics in Honor of G erad Debreu, W. Hildenbrand and A. Mas-Colell, eds, North Holland, Amsterdam, 205--223, 1986.

....Option valuation is no longer preference free and one has to make assumptions concerning the pricing of volatility risk. Since the two sources of risk in our model are uncorrelated, we assume that volatility risk is not priced. This corresponds to the choice of the minimal martingale measure of Follmer and Sondermann (1986) and Follmer and Schweizer (1991) a consequence of which is that every nontradable asset is not priced, see also Theorem 3.1 of Hofmann, Platen and Schweizer (1992) Under this assumption, the option price is C(S t ; t) E[CBS (S t ; t; V ) j F t ] 11) Z IR CBS (S t ; t; V )dH( V j ....

....GARCH volatility on option prices. In particular, it will be of interest to compare the impact of positive and negative autoregression parameters on option prices. A further appealing property of Duan s approach is that the weak limit of his martingale measure is the minimal martingale measure of Follmer and Sondermann (1986) and Follmer and Schweizer (1991) see Duan (1996) Many bivariate diffusion models, such as the Hull and White (1987) model, may be recovered from Duan s model. A general result is that volatility risk is not priced unless volatility and stock price changes are correlated, as in the TGARCH case. ....

Follmer, H., D. Sondermann (1986), Hedging of Non-redundant Contingent Claims, in: Hildenbrand, W., Mas-Colell, A. (eds.), Contributions to Mathematical Economics, Amsterdam, North Holland, 205--223.

....interpretation of (1.2) if the martingale representation property w.r.t. X does not hold, the variable N1 in (1.2) is in general not equal to 0. We are in the incomplete model case, and the process is shown to be a risk minimizing strategy for hedging the claim U : see Follmer and Sondermann [7]. 3) Let us now turn to convergence results. To get an idea of what to expect as far as convergence results are concerned, here is a trivial special case: we have a sequence U n of random variables tending to a limit U in IL 2 (P ) and a fixed locally square integrable martingale X. Writing ....

Follmer H. and Sondermann D.: Hedging of non redundant contingent claims. In Contributions to Mathematical Economics, eds W. Hildebrand and A. Mas-Colell, 205-223, 1986.

....# is allowed to be adapted, this condition can always be satisfied by choice of # T . But since such strategies will not be self financing, a good strategy should now have a small cost process C. To measure the riskiness of a strategy, the use of a quadratic criterion was first proposed by Follmer Sondermann (1986) for the case where X is a martingale and subsequently extended to the general case in Schweizer (1991) Under certain technical assumptions, such a locally risk minimizing strategy can be characterized by two properties: its cost process C should be a martingale (so that the strategy is no ....

H. Follmer and D. Sondermann (1986) "Hedging of non-redundant contingent claims", in: W.

....of our marked point process model. Since our market is incomplete due to the presence of jumps and stochastic jump intensity, we have to choose some approach to hedging derivatives under incompleteness to determine hedging strategies. Here we use the criterion of risk minimization proposed by F ollmer and Sondermann (1986). In contrast to most of the previous literature we assume in the present paper, that the hedger has only access to the information contained in past asset prices. While this assumption is perfectly realistic from an economic viewpoint, it causes di culties for the computation of hedge strategies ....

....and A3 are satis ed; hence the asset price is a square integrable martingale. Since our market is incomplete we have to choose some approach to hedging derivatives under incompleteness to determine hedging strategies. In this paper we shall use the criterion of risk minimization as analyzed in F ollmer and Sondermann (1986) and F ollmer and Schweizer (1991) We consider the case where the hedger has only access to the information contained in past asset prices, i.e. to the ltration fF S t g. While this assumption is perfectly realistic from an economic viewpoint, it causes di culties for the computation of hedging ....

[Article contains additional citation context not shown here]

F ollmer, H., and D. Sondermann (1986): \Hedging of non-redundant ContingentClaims, " in Contributions to Mathematical Economics, ed. by W. Hildenbrand, and A. Mas-Colell, pp. 147-160. North Holland.

....and Renault (1998) On the other hand, Nelson (1990) proved that by shrinking the time interval to zero, GARCH models converge to bivariate diffusions. Pricing in the bivariate diffusion case has been the topic of a whole branch of literature in the mathematical finance community, starting with Follmer and Sondermann (1986) and Follmer and Schweizer (1991) Independent of the time series literature, stochastic volatility models have been proposed, for example, by Hull and White (1987) Chesney and Scott (1989) and Heston (1993) For the purpose of valuation and hedging in these stochastic volatility models, the ....

F ollmer, H., and D. Sondermann (1986): "Hedging of Non--Redundant Contingent Claims," in Contributions to Mathematical Economics, ed. by W. Hildenbrand, and A. Mas-Colell, chap. 12, pp. 205--223. North--Holland.

....e and Shreve [26] Local) Risk Minimization Even in an incomplete market a part of the risk incurred by selling derivatives can be hedged by dynamic trading in the underlying asset. In the theory of (local) risk minimization which has been developed in the papers F ollmer and Sondermann [34] Schweizer [64] and F ollmer and Schweizer [33] one seeks to find a trading strategy that reduces the actual risk of a derivative position to some intrinsic component. While the computation of the strategy usually involves the computation of prices for contingent claims, the focus of this ....

....( j ) with terminal value equal to H that minimizes at each time t the remaining risk R t : E P [ C T Gamma C t ) 2 jF t ] 39) Here the minimization is over all admissible continuations of ( j ) after t with terminal value equal to H . F ollmer and Sondermann [34] have studied existence and uniqueness of such a strategy if the stock price process is a P martingale. In that case a unique risk minimizing strategy exists. It can be computed by means of the well known Kunita Watanabe decomposition 14 of the P martingale H t = E P [ HjF t ] with respect ....

F ollmer, H., and D. Sondermann (1986). Hedging of non-redundant Contingent-Claims, in Contributions to Mathematical Economics , ed. by W. Hildenbrand, and A. Mas-Colell, pp. 147--160. North Holland.

....beyond the need to enforce positivity and, sometimes, mean reverting behaviour for the process. This and the fact that a whole unknown and utterly unobservable function (x; v; t) has to be estimated in general in order to price consistently with this theory, has led us and other researchers [1, 15, 24] to new approaches to translating uncertain volatility risk into price. We address this in Section 3. 2 Smile Curve Definition Given a price C(K; for a European option with time to maturity = T Gamma t and strike price K (from, say, market data or a different pricing model) we can ....

....costs involved in purchasing the other derivative. Romano Touzi [33] looked for an optimal second option strike price to hedge with to lower such costs, and Renault Touzi [32] studied the effects of just hedging with the underlying stock. Another line of research by Follmer Sondermann [15] and Schweizer [36] tackles the implicit uncertainty of how to hedge represented by the dependence of the pricing measure Q( oe ) on the volatility risk parameter oe (see expression (1.2) by choosing the measure that minimises the expected variance of the cost of hedging with just the ....

H. Follmer and D. Sondermann. Hedging of non-redundant contingent claims. In W. Hildenbrand and A. Mas-Colell (eds.), Contributions to Mathematical Economics, pages 205--223, 1986.

No context found.

Follmer H. and Sondermann D., 1986, "Hedging of non-redundant contingent claims".

No context found.

H. Follmer and D. Sondermann, "Hedging of non-redundant contingent claims", Contributions to Mathematical Economics, 1986, pp. 205-223.

No context found.

Follmer, H., Sondermann, D. (1986): Hedging of non-redundant contingent claims. In: Mas-Collel, A., Hildebrand, W. (eds.), Contributions to Mathematical Economics, 205-223. North Holland, Amsterdam.

No context found.

Follmer, H., Sondermann, D. (1986): Hedging of non-redundant contingent claims. In: Mas-Collel, A., Hildebrand, W. (eds.), Contributions to Mathematical Economics, 205-223. North Holland, Amsterdam.

No context found.

Follmer, H. and D. Sondermann (1986): Hedging of Non-Redundant Contingent Claims. In "Contributions to Mathematical Economics", (Mas-Collel A. and Hildebrand W. Editors). Amsterdam: North Holland, 205-223.

No context found.

F/Jllmer, H. and Sondermann, D. (1986): Hedging of non-redundant contingent claims. In: Contributions to Mathematical Economics. Eds: W. Hildenbrand and A. Mss Coilell, pp, 205-223

No context found.

F#ollmer,H. & D. Sondermann #1986#. Hedging of non-redundant contingent claims. In W. Hildebrandt and A. Mas-Colell #Eds.#,Contributions to Mathematical Economics, pp.205#223. North Holland.

No context found.

Follmer, H. and D. Sondermann, 1986, "Hedging of Non-Redundant Contingent Claims," In Contributions to Mathematical Economics in Honor of Gerard Debreu, W. Hildenbrand, A. Mas-Colell, eds. North Holland, Amsterdam, 205-223.

No context found.

Follmer, H., Sondermann, D.: Hedging of non-redundant contingent claims. In: Mas-Colell, A. and Hildenbrand, W. (eds): Contributions to Mathematical Economics. North-Holland, Amsterdam, 1986, pp. 205-223

No context found.

Follmer, H., Sondermann, D.: Hedging of non-redundant contingent claims. In: Hildenbrand, W., Mas-Colell, A. (eds.): Contributions to Mathematical Economics. Amsterdam: North-Holland 1986, pp 205-223

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC