A geometric Brownian motion with drift and volatility is defined by the equation ds =...

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A geometric Brownian motion with drift μ and volatility is defined by the equation ds = µSdt +oSdze Ito's lemma states that if G is a function of S and t, then ƏG OG 10²G + ƏG (25μs +. at zasz²52dt +. The Black-Scholes differential equation for currency derivatives is given by as asdz af at + (-)Sa+ af 1 ²520²f where r, is the interest rate in the domestic country and r, is the interest rate in the foreign country. asz=rof dG = Explain 1-1.Discuss the main assumptions of the Black-Scholes option pricing model. concept of arbitrage and the arbitrage condition underlying the Black-Scholes differential equation. the 1-2 Let F, be the arbitrage-free forward exchange rate on a currency forward contract with time to expiration (T-t) and f, be the value of a forward exchange contract with a strike of K (L.e. a contract to buy one unit of the foreign currency in exchange for K units of the domestic currency). Derive the stochastic processes followed by F, and f, and explore whether they are geometric Brownian motion processes. 1-3Consider an exchange rate derivative with the following theoretical price! d₂ = S₂e(re-TD)(T-t) From the perspective of an arbitrageur, examine whether this function could be the price of a traded derivative. Explain your approach. A geometric Brownian motion with drift μ and volatility is defined by the equation ds = µSdt +oSdze Ito's lemma states that if G is a function of S and t, then ƏG OG 10²G + ƏG (25μs +. at zasz²52dt +. The Black-Scholes differential equation for currency derivatives is given by as asdz af at + (-)Sa+ af 1 ²520²f where r, is the interest rate in the domestic country and r, is the interest rate in the foreign country. asz=rof dG = Explain 1-1.Discuss the main assumptions of the Black-Scholes option pricing model. concept of arbitrage and the arbitrage condition underlying the Black-Scholes differential equation. the 1-2 Let F, be the arbitrage-free forward exchange rate on a currency forward contract with time to expiration (T-t) and f, be the value of a forward exchange contract with a strike of K (L.e. a contract to buy one unit of the foreign currency in exchange for K units of the domestic currency). Derive the stochastic processes followed by F, and f, and explore whether they are geometric Brownian motion processes. 1-3Consider an exchange rate derivative with the following theoretical price! d₂ = S₂e(re-TD)(T-t) From the perspective of an arbitrageur, examine whether this function could be the price of a traded derivative. Explain your approach.