本书内容如下为例:
CHAPTER 2: STANDARD PRICING RESULTS
UNDER DETERMINISTIC AND STOCHASTIC
INTEREST RATES
Along with providing the way uncertainty is formalized in the considered
economy, we establish in this chapter the assumptions that will be adopted
throughout Part I of this book and the general principles governing asset
pricing (§1), then the relationship between the spot and the forward prices of
a risky asset (§2), and lastly that between the spot and the futures prices
(§3). Any dividend (or coupon, or convenience yield) will always be
assumed both continuous and deterministic.
2.1. GENERAL SETTING AND MAIN ASSUMPTIONS
In this framework, individuals can trade continuously on a frictionless
and arbitrage free financial market until time xE, the horizon of the economy.
A locally riskless asset and a number n of pure default-free discount bonds
sufficient to complete the market are traded. The latter pay one dollar each at
their respective maturities, respectively Tj, j = 1,..., n, with Tj_i < Tj < xE.
The following sets of assumptions provide the necessary details.
Assumption 1: Dynamics of the primitive assets.
- At each date t, the price P(t,Tj) of a discount bond whose maturity is Tj ,
j = 1,..., n, is given by :
p(t,Tj)=exp[-{Tjf(t,s)ds] (1)
where f(t,s) is the instantaneous forward rate (thereafter the forward rate)
prevailing at time t for date s, with t < s < xE.
- The instantaneous spot rate (thereafter the spot rate) is r(t) = f(t,t).
Agents are allowed to trade on a money market account yielding this
continuous bounded spot rate. Let B(t) denote its value at time t, with
B(0)=l.Then:
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