Stock Price Is Currently
FIN 441 Practice Final(Must show calculations in detail to earn credit)1. The price of a put option decreases when interest rates rise. Explain why.(7 points)~Chapter 3-slide 54~ Because the stock price increases when interest rate rise and a put (right to sell) option locks in a stock price. When the stock price increases your profit decreases. There is a negative relation between put price & interest rate.2. A stock price is currently $100. Over each of the next years it is expected to go up by 4.88% or down by 2.53%. The risk-free interest rate is 2.5% per annum. What is the value of a two-year American put that has a strike price of $100?(15 points) Answer: $0.79S0=$100 X=$100 r=2.5% n=2 u=1.0488 (1+.0488) d=.9747 (1-.0253)Su=104.88Su2=100*(1.0488^2)=109.998Sd=97.47Sd2=100*(.9747^2)=95.004Sud=100*1.0488*.9747=102.227Pu2=Max[0,X-Su2]=100-109.998=-9.998=0Pd2=100-95.004=4.996Pud=100-102.997=-2.227=0P=(1+.025-.9747)/(1.0488-.9747)=.0503/.0741=.6788p=1-.6788=.3212Pd=(.6788*0+((.3212*4.996)/1+.025)=0+(1.6047/1.025)=1.5656Pu=.6788*0+(.3212*0/1.025)=0+0=0P=.6788*0+((.3212*1.5656)/1.025)=0+.50287/1.025=0+.4906=.4906100-97.47=2.53P=0+((.3212*2.53)/1.025)=0+.81264/1.025=.79
3. Would an American call be worth more than its European counterpart if the stock (a) does not pay dividend and (b) does pay dividend? Explain.(7 points)~Chapter 3: slides 27-31~a)Equal-Holding the call is insurance against stock price decreases by the end of the holding periodb)Yes-the investor would want to exercise the call before the ex-dividend date and you can only do this with an American call4. Would an American put be worth more than its European counterpart if the stock (a) does not pay dividend and (b) does pay dividend? Explain.(7 points)~Chapter 3: slide 53~a)Equal-b)Yes-the investor would want to exercise immediately after the ex-dividend date which you can only do with an American put5. Why do higher interest rates lead to higher call price but lower put prices?(7 points)~Forward/Futures pdf: page 13~Higher interest rates give a higher profit for a call and a lower profit for a put6. If the futures price is lower than the spot price plus carrying cost, is there an arbitrage opportunity? If so, design a trading strategy. (7 points)