H. E. Leland. Option pricing and replication with transaction costs. Journal of Finance, 40:1283--1301, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the expected costs of changing the delta hedged position at the end of the hedging interval. In general this equation is nonlinear and must be solved numerically. However, when actual returns are specified the gamma, V SS , is always positive and we can simply use the Leland volatility correction [15]: # Leland = # 1 ##t hedge 1 2 . 37) Even when log returns were specified, the regions where the gamma changes sign are so far away from the region of interest (see Figure 3(b) that we could not notice any di#erences between the solution computed using (36) compared with the ....

H. Leland. Option pricing and replication with transaction costs. Journal of Finance, 40:1283--1301, 1985.

....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 basis risk completely. Even ....

H.E. Leland, Option Pricing and Replication with Transaction Costs, Journal of Finance 40 n.5 (1985) 1283-1301

....a portfolio with partially offsetting positions will incur less total transaction costs than hedging all of the constituent contracts individually. However, it has been shown that a good approximation for the case of noticeable bid offer spread is to use an appropriately increased volatility [Lel85, NK97, BV92, Wil98]. Also, the assumption of linearity is still justifiable in the presence of non negligible bid offer spreads if the portfolio only contains instruments of the same monotonicity of pay offs, i.e. only plain vanilla call options or only plain vanilla put options of different strikes and maturities ....

H. E. Leland. Option pricing and replication with transaction costs. Journal of Finance, 40:1283--1301, 1985.

....into account transaction costs and that is equal to a Black Scholes price but with a modi ed volatility of the form = 0 (1 cA) 1=2 ; A = 0 p 4t ; with c = 1. Here, is the proportional transaction cost, 4t the transaction period, and 0 is the original volatility constant. Leland [23] computed the constant c = 2= 1=2 . Kusuoka [19] then showed that the optimal c depends on the risk structure of the market. Another approach is the maximization of the utility function. For instance, Davis et al. 9] compute the option price as the solution of a nonlinear quasivariational ....

H. Leland. Option pricing and replication with transaction costs. J. Finance 40, 1283-1301, 1985.

....for example, Detemple and Murthy #1997#. 2: Portfolio choice and option hedging in the presence of proportional transactions costs have been studied, respectively, by Constantinides #1986#, Davis and Norman #1990#, and Dumas and Luciano #1991# with a somewhat di#erent optimality criteria, and by Leland #1985#, Merton #1989#, Shen #1990#, and Boyle and Vorst #1991# without an explicit optimality criteria. 3: Leverage and nonnegative wealth constraints are analyzed by Grossman and Vila #1992# and Cox and Huang #1989#, respectively, with a somewhat di#erent optimality criterion. 4: In continuous time ....

LELAND H.E. #1985#, #Option Pricing and Replication with Transaction Costs", Journal of Finance, 49, 1283-1301.

....of superhedging strategies in models with uncertain but bounded volatility is a special case of (4.2) In their model we have v(t; S; q) 1 fq 0g 1 fq 0g ; where and represent a lower and upper a priori bound on the otherwise unspeci ed asset price volatility. Transaction costs: Leland (1985), Hoggard, Whalley, and Wilmott (1994) and in particular Barles and Soner (1998) have given asymptotic results which provide a characterization of the replication cost for a derivative in a Black Scholes model with proportional transaction costs in terms of nonlinear PDE s which are all of the ....

Leland, H. (1985): \Option Pricing and Replication with Transaction Costs," Journal of Finance, 40, 1283-1301.

....a certain condition. The positivity of such diagonal entries has an important e ect on the stabilization of the numerical scheme. 2. 3 Models with transaction costs We consider a vanilla American option with proportional transaction costs cast in the periodic rebalancing framework of Leland [20]; see also [26, Chapter 13] and [16] Let t 0 be a nite xed time step so that the portfolio is revised every t; the random walk of the asset price in discrete time is assumed to be: S = S t S p t; where is a random variable with a standardized normal distribution. Let k 0 denote ....

H.E. Leland, \Option pricing and replication with transaction costs", Journal of Finance 40 (1985) 1283-1301.

....solutions theory that we apply, turn out to be a very powerful and a very simple to use tool in this particular problem. The approach also enables us to give another interpretation to the well known connection between hedging with a modified volatility and hedging under transaction costs (see Leland (1985), Avellaneda and Par as (1994) Barles and Soner (1995) In fact, we were motivated to use our approach after having applied it successfully to a similar problem in a stochastic volatility framework in Cvitani c, Pham and Touzi (1997) Although the type of results we get are negative and ....

....fixed (a; y) 2 IR 2 , the partial differential equation v t 1 2 x 2 oe(t; x; y) a f 0 (y) f(y) 2 v xx = 0 with a terminal condition, characterizes the Black Scholes price when the underlying asset has the adjusted price process X a;b . This is consistent with the result of Leland (1985) which shows that the option price under transaction costs of order p Deltat, Deltat being the time space between transaction dates, corresponds to a Black Scholes price with an adjusted volatility. Therefore, taking the supremum over a 2 IR can be interpreted as the super replication price in ....

Leland, H.E. (1985) "Option pricing and replication with transaction costs", J. Finance 40, 1283-1301.

....fx 2 R d : x = b(S)c; c 2 Cg, which implies W (S; T ) 0. So, by the maximum principle, W 0 everywhere. Optimal Replication of Contingent Claims Under Portfolio Constraints 20 Footnotes 1. The effect of transactions costs on option pricing and hedging has been studied in discrete time in Leland (1985), Boyle and Vorst (1992) Edirisinghe, Naik, and Uppal (1993) Boyle and Tan (1994) Barles and Soner (1995) and Rutkowski (1996) In continuous time transactions costs are treated in Flesaker and Hughston (1993) Wilmott, Dewynne, and Howison (1993) Cvitani c and Karatzas (1996) and Soner, ....

Leland, H., 1985, "Option Pricing and Replication with Transactions Costs," Journal of Finance, 40, 1283--1301.

....costs (their payoff could always be attained by following the appropriate dynamic trading strategy) A couple of different approaches for handling transaction costs have been proposed. The simplest approach involves assuming that the replicating portfolio is adjusted at fixed points in time (e.g. [15, 5, 20]) More sophisticated models involve determining when to optimally adjust the replicating portfolio (e.g. 10, 8] For present purposes, the simpler approach is of some interest because it leads to a nonlinear PDE of the same form as the uncertain volatility model. Previously, explicit methods ....

....a short position (a negative payoff) in the option is given by the negative of the solution to equations (1) and (5) Consequently, the worst best long case prices would correspond to the bid ask prices for an option if the buyers sellers priced the option assuming worst case scenarios. The Leland [15] transaction cost model was extended for arbitrary payoffs in [11, 23] In this case, the value of a long position is given by the solution to U t oe 2 c 2 S 2 [1 Gamma ff sgn( Gamma) U SS rSU S Gamma rU = 0 (6) and that of a short position is U t oe 2 c 2 S 2 [1 ff ....

H.E. Leland. Option pricing and replication with transaction costs. J. Fin., 40:1283--1301, 1985.

....by Marco Avellaneda and Antonio Par as 1 Abstract: We introduce a new class of strategies for hedging derivative securities in the presence of transaction costs assuming lognormal continuous time prices for the underlying asset. We do not assume necessarily that the payoff is convex as in Leland [11] or that transaction costs are small compared to the price changes between portfolio adjustments, as in Hoggard, Whalley and Wilmott [8] The type of hedging strategy to be used depends on the value of the Leland number A = q 2 k oe p ffit , where k is the round trip transaction cost, oe ....

....transaction costs cannot be ignored without incurring in risk or loss. This is an important practical problem, especially in emerging markets where roundtrip transaction costs of 1 and higher are not uncommon. In 1985, Leland introduced a theory for pricing a call option with transaction costs [11]. Using an elegant argument, he showed that the price of a call is given by the Black Scholes formula with an augmented volatility oe A = oe p 1 A ; where A = r 2 Delta k oe p ffit : Here, oe represents the volatility of the underlying security, k is the round trip transaction cost ....

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H. E. Leland, "Option Pricing and Replication with Transaction Costs", J. of Finance, 40, 1283-1301 (1985)

....in terms of desired asset proportions, such as a 60 40 ratio of stocks to bonds, or 40 40 20 proportions of domestic assets, foreign assets, and cash. As asset values move randomly, asset ratios diverge from their targets. But when asset returns follow a diffusion process, it is well known (e.g. Leland [1985]) that an infinite amount of trading is required to keep assets continuously at their target proportions. This creates a problem: frequent readjustments to keep assets close to their target levels will incur high trading costs. But infrequent revision will create tracking error relative to the ....

....to the optimum ratio: the gain is of second order, and insufficient to justify the (first order) trading costs. 2 Related problems include the optimal cash management problem examined by Connor and Leland [1995] and the option replication problem in the presence of transactions costs (see, e.g. Leland [1985] and Hodges and Neuberger [1989] 3 An ad hoc approach has been to adjust the mean return of an asset or asset class downwards to reflect trading costs. This approach is erroneous, as discussed in Section X. 4 See, for example, Grinold and Kahn (1995) 4 Second, we develop a technique for ....

Leland, H. [1985], "Option Pricing and Replication with Transactions Costs," Journal of Finance 40, 1283-1302.

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Leland H. Option pricing and replications with transactions costs. Journal of Finance, XL, 5, 1985, 12831301.

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H. E. Leland. Option pricing and replication with transaction costs. Journal of Finance, 40:1283--1301, 1985.

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Leland H., 1985, Option Pricing and Replication with Transactions Costs, The Journal of Finance, 40, 1283-1301

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Leland, H. (1985). "Option pricing and replication with transaction costs", Journal of Finance 40, pp. 1283-1301.

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Leland H.E. (1985), Option Pricing and Replication with Transaction Costs, Journal of Finance, vol. 40, 1283-1301.

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Leland H.E. (1985), Option Pricing and Replication with Transaction Costs, Journal of Finance, vol. 40, 1283-1301.

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