# Download Options, Futures and Exotic Derivatives (Frontiers in by Eric Briys, Mondher Bellalah, Huu Minh Mai, Fran?ois de PDF

By Eric Briys, Mondher Bellalah, Huu Minh Mai, Fran?ois de Varenne

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Extra info for Options, Futures and Exotic Derivatives (Frontiers in Finance Series)

Example text

According to (1), the dynamics of return of the default-free zero-coupon bond P(t, T) maturing at time Tis given at time t under Q by dP(t, T) r(t)dt = -os(t, T)dW,(t) (2) T) is a deterministic function defined by T)=o(t) og(t, a(s)ds exp du (3) We let B(t) represent the value as of time t of a portfolio which, at date t 0, has invested one dollar, continuously reinvested at the prevailing spot interest rate r(t). In other words, the B(t) fund defines a capitalization factor over time. It is given by = Economy There are two sources of uncertainty across the economy, represented by two independent standard Brownian motions, (Wi(t), W2(t), TE [0.

We consider a very general economy where transactions are continuous on a givea áme period [0, T]. This economy is characterized by the following four assumptions. NUMERAIRE CHANGING continuously discounted price of any security probability. 4) Dynamics = exp r(u)du (4) of the Risky Asset . Let us assume that there is a risky asset A, in the economy, price dynamics under the risk-neutral probability Q: characterized by the following . d A, = r(t)dt + aa[p d Wi(t) + - d W2(t)] (5) where as denotes the instantaneous standard deviation of the asset return.

O(t) is the instantaneous standard deviation of r(t). According to (1), the dynamics of return of the default-free zero-coupon bond P(t, T) maturing at time Tis given at time t under Q by dP(t, T) r(t)dt = -os(t, T)dW,(t) (2) T) is a deterministic function defined by T)=o(t) og(t, a(s)ds exp du (3) We let B(t) represent the value as of time t of a portfolio which, at date t 0, has invested one dollar, continuously reinvested at the prevailing spot interest rate r(t). In other words, the B(t) fund defines a capitalization factor over time.