D. Lamberton and B. Lapeyre. Introduction to stochastic calculus applied to nance. Chapman & Hall, London, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... asset follows a continuous 1 factor diffusion process with the initial value S init : 0, # ] for some fixed time horizon [0, # ] W t is a Brownian motion, and (s, t) # # (s, t) are deterministic functions sufficiently well behaved to guarantee that (1) has a unique solution [23]. Note that in this notation # # (s, t) can be negative as well as positive. The conventional notion of positive volatility corresponds to # # (s, t) in our notation. For simplicity, we assume that the instantaneous interest rate is a constant r 0 and the dividend rate is a constant q ....

D. LAMBERTON AND B. LAPEYRE, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall, 1996.

....with respect to t G . Hence, we have shown that t r follows the CIR process given by (3.4) Similarly, we have that ( tttt dabdt2dMl= l sl # # , 3.8) where d b 4 s q # # . The CIR process has two properties that correspond with empirical spot rates and risk spreads. First, it is shown in (Lamberton Lapeyre, 1996) that the CIR processes (3.4) and (3.8) are almost surely positive, provided that d 2, 0 r0 , and 0 0 l almost surely. Unfortunately, in the one dimensional case we have that the probability that these CIR processes vanish for infinitely many times is one. The second ideal property of the CIR ....

Lamberton, D. & Lapeyre, B. (1996) Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall, New York.

....reasoning, the solution to an appropriate free boundary problem is taken as a candidate price for the option at hand. Then this solution is shown to be equal to the supremum (1.4) as a consequence of it being a solution to the free boundary problem. Fluctuation theory appoach. The second approach [19, 12], used for evaluating American call and put options, consists of proving that the optimal stopping time has the form of a hitting time of the stock price at some level, say a. Given that (K Gamma S t ) or indeed (S t Gamma K) is constant at such a hitting time, the price of the option ....

....title of this paper, in effect constitutes only half of the pricing procedure. There is still a strength of optimal stopping theory found in Theorems 1.2 and 1.3 which give the foundation on which we build. For standard references in the context of these the reader is referred to [18] 16] and [12]. 4 2 Perpetual Call and Put Options Combining Theorem 1.2 with the actual form of the system of payments for call and put (1.2) we find by a simple Markovian decompostion of the process S t that the the price Pi call ; Pi put of a perpetual call and put satisfy (1.6) where Pi call ....

Lamberton, D. and Lapeyer, B. (1996) Introduction to Stochastic Calculus Applied to Finance. Chapman and Hall.

....probability of a single obligor 1.4.1 The Merton model Merton tackled the problem of pricing and hedging a European Call option on a non dividend paying stock if the stock value followed a geometric Brownian Motion. If the reader requires more details as a reminder of this section, see [15] and [17]. Under the no arbitrage assumption there exists a unique self financing trading strategy which replicates the value of the Call at maturity, assuming trading is possible in a continuous manner and is only allowed in the stock (the risky asset) and in a risk free asset, the bank account. The ....

Lamberton, D., Lapeyre, B. (1996): Introduction to Stochastic Calculus applied to Finance. Chapman & Hall, London.

.... motion, can turn to texts like [9] and [18] where the basic concepts are presented via discrete trees; at any instant of time the price process can visit only a nite number of states (typically up or down) Very readable texts introducing the Brownian motion based models are for instance [2, 22, 26, 28]. References to more advanced literature are given at the end of the sections below. In [3, 24] some interesting historical discussions on the subject of derivatives and nancial risk can be found. Nick Dunbar in [10] gives an excellent historical account of the events leading up to and ....

Lamberton, D. and Lapeyre, B. (1996). Introduction to Stochastic Calculus Applied to Finance. Chapman and Hall, London.

....Although the Fundamental Theorem of Asset Pricing crucial for the foundation of the theory as the name rightly indicates it only is the door opener to a wide range of questions. For a more comprehensive presentation of this fast growing field we refer to the recent text book literature (e.g. [LL96], MR97] B98] KS98] S99] and the references given there) 2 Strategies and Arbitrage Possibilities As stated in the introduction the main ingredient in arbitrage theory is stochastic integration. In this section we will give a mathematical formulation of the objects referred to in the ....

Lamberton, D., Lapeyre, B. Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall (1996).

.... the initial value S init : dS t S t = S t , t)dt # # (S t , t)dW t , t # [0, # ] for some fixed time horizon [0, # ] W t is a Brownian motion, and (s, t) # # (s, t) # [0, # ] # # are deterministic functions sufficiently well behaved to guarantee that (1) has a unique solution [23]. Note that in this notation # # (s, t) can be negative as well as positive. The conventional notion of positive volatility corresponds to # # # (s, t) 2 in our notation. For simplicity, we assume that the instantaneous interest rate is a constant r 0 and the dividend rate is a constant q ....

D. LAMBERTON AND B. LAPEYRE, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall, 1996.

.... the initial value S init : dS t S t = S t , t)dt # # (S t , t)dW t , t # [0, # ] for some fixed time horizon [0, # ] W t is a Brownian motion, and (s, t) # # (s, t) # [0, # ] # # are deterministic functions sufficiently well behaved to guarantee that (1) has a unique solution [24]. Note that in this notation # # (s, t) can be negative as well as positive. The conventional notion of positive volatility corresponds to # # # (s, t) 2 in our notation. For simplicity, we assume that the instantaneous interest rate is a constant r 0 and the dividend rate is a constant q ....

D. LAMBERTON AND B. LAPEYRE, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall, 1996.

....to the equation X t = x Z t 0 (a bX s ) ds oe Z t 0 q X s dW s ; 0.6) for t 0; a 0; oe 0. In the finance literature this process is known as the Cox Ingersoll Ross (CIR) process. For a treatment of interest rate models including the CIR model we refer to Lamberton Lapeyre [18], x6. We remark that this process is also used in a population growth model, see Karlin Taylor [15] p. 334. The CIR process is a space time transformed BESQ process, more explicitly: A BESQ ffi (y) process Y can be transformed to the CIR process X by X t = e bt Y oe 2 4b (1 Gamma e ....

Lamberton, D. and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall, 1996.

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D. Lamberton and B. Lapeyre. Introduction to stochastic calculus applied to nance. Chapman & Hall, London, 1996.

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B. Lapeyre, D.Lamberton. An Introduction to Stochastic Calculus Applied to Finance, Chapman and Hall, (1995).

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D. Lamberton D., B. Lapeyre, Introduction to Stochastic Calculus applied to Finance, Chapman & Hall, 1996, 185p.

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Lamberton, D., and Lapeyre, B. (1996) Introduction to Stochastic Calculus Applied to Finance, Chapman&Hall, London.

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D. Lamberton, B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall 1997.

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Lamberton D. and Lapeyre B., Introduction to stochastic calculus applied to ...- nance, Chapman and Hall, London, 1995.

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Finance, 1, No. 1, 13--25. Lamberton, D., and B. Lapeyre (1996): Introduction to Stochastic Calculus Applied to Finance. London: Chapman & Hall.

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