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plot the payoff diagrams fur the following instrumentsa a caplet with cap rate rcap 675 written on 3-wonth libor lt
in this exercise we work with the black-scholes setting applied to foreign currency denominated assets we will see a
assume that the return rt of a stock has the following log-normal distribution for fixed tlog rt nmu sigma2suppose we
consider a random variable x with the following values and the corresponding probabilitiesdeltax 1 pdeltax 1 3deltax
considernbspwhere xt is an exponential wiener processa calculate the expected value of the increment dztb is zt a
this exercise deals with obtaining martingales suppose xt is a geometric process with drift mu and diffusion parameter
the exercises in this section prepare the reader for the next three chapters instead of dealing with the pdes an
a function fx z y t of four variables x z y t that satisfy the following pde is called the heat equationwhere a is a
you are given a function fx z y of three variables x z y the following pde is called laplaces equationaccording to this
consider the linear sde that represents the dynamics of a security pricedst 01 stdt 05 stdwtwith s0 1 givensuppose a
consider the geometric sdedst mustdt sigmastdwtwhere st is assumed to represent an equity index the current value of
let h be a wiener process consider the geometric process s againa calculate dstb what is the expected rate of change of
we consider the random process st which plays a fundamental role in biack-scholes analysesst s0emu1sigmawtwhere wt is
you are given the representationwhere the equality holds given the sequence of information sets it the underlying
let wf be a wiener process and t denote the time are the following stochastic
let y be a random variable withnbspey lt infina show that the mt defined bymt eyitis a martingaleb does this mean that
a random variable z ahs poisson distribution ifnbsppk pz lt k lambdake-k kfor k 0 1 2 nbspa use the expansionto
we say that z is exponentially distributed with parameter a gt 0 in the distribution function of z is given bypz lt z
you are given the price of a nondividend paying stock st and a european call option ct in a world where there are only
an at-the money call written on a stock with current price st 100 trades at 3 the corresponding at-the -money put
victoria bond is a premium bond with 8 coupon houston bond is a 4 coupon bond currently selling at a discount both
let the arbitrage-free 3-month futures prices for wheat be denoted by ft suppose it costs c to store 1 ton of wheat for
consider a fixed-payer plain vanilla interest rate swap paid in arrears with the following characteristics1 the start
consider the following investmentsan investor short sells a stock at a price s and writes an al-the-money call option
suppose you are a director of an energy company that has three divisions-natural gas oil and retail gas stations these