Question 2: Arbitrages (50%) Maya is a taxi driver and has no money to invest in financial markets. However, she has been studying economics remotely and has a knack for business. With her smartphone and a trading app, she can easily trade two assets: a dollar-denominated riskfree discount bond issued by a local government in the region, and a global equity index fund (all paying in dollars tomorrow'). Currently, the discount bond trades at 98 cents per dollar of face value. Her friend Hedi strongly believes that the world economy is at a turning point. If US presidential hopeful Joe Biden wins, the US economy will take off and the global equity index fund will increase by 2%. If Biden loses, on the other hand, the economy will tank, and the global index fund will lose 3% of its value. After watching CNN, he believes Biden will win with 60% probability. "Do not waste your time with the app," Hedi says "There is no money to make with these prices, my cousin Malik is a finance wizard working in Dubai and he told me he is sure about the scenarios I laid out in front of you. Plus, you have no money to invest!" a) (10 pts) Should Maya follow her friend's advice? Explain. b) (10 pts) "Prices are competitive over this trading platform. They are quoted to match demand and supply. They are equilibrium prices. Is this true? Explain. A few hours later, Hedi comes back to check on his friend Maya. He heard someone made some cash with a call option on the global index fund and which has an exercise price of USD 100.5 and expires on Nov 4, 2020. He claims he wants to sell such an option to her at a price of USD 1. The market estimates on the global index are still valid, but the discount bond price has climbed to 99 cents, and the index is quoted at 100. c) (10 pts) Should Maya buy the call option from Hedi? If she only has access to the discount bond and the index mentioned above, but she can buy and sell these assets short via the app, how can she finance this purchase without borrowing money from her family? d) (10 pts) What is the market estimate of Biden's probability of winning the elections? A couple of days later, Maya talks directly to Malik. His firm has estimated the two assets payoff matrix to be 1 2 A= 1 -1 -1 (note: there are now multiple economic scenarios relevant for the trading period) and prices now are q = (.5,1). e) (10 pts) Can you spot an arbitrage for Maya to invest in? Does the Law of One price hold on the trading platform now? Is there an s-arbitrage for s = 12 Numerically compute an arbitrage portfolio, if any exists. Explain, and show your results using a graph. Question 2: Arbitrages (50%) Maya is a taxi driver and has no money to invest in financial markets. However, she has been studying economics remotely and has a knack for business. With her smartphone and a trading app, she can easily trade two assets: a dollar-denominated riskfree discount bond issued by a local government in the region, and a global equity index fund (all paying in dollars tomorrow'). Currently, the discount bond trades at 98 cents per dollar of face value. Her friend Hedi strongly believes that the world economy is at a turning point. If US presidential hopeful Joe Biden wins, the US economy will take off and the global equity index fund will increase by 2%. If Biden loses, on the other hand, the economy will tank, and the global index fund will lose 3% of its value. After watching CNN, he believes Biden will win with 60% probability. "Do not waste your time with the app," Hedi says "There is no money to make with these prices, my cousin Malik is a finance wizard working in Dubai and he told me he is sure about the scenarios I laid out in front of you. Plus, you have no money to invest!" a) (10 pts) Should Maya follow her friend's advice? Explain. b) (10 pts) "Prices are competitive over this trading platform. They are quoted to match demand and supply. They are equilibrium prices. Is this true? Explain. A few hours later, Hedi comes back to check on his friend Maya. He heard someone made some cash with a call option on the global index fund and which has an exercise price of USD 100.5 and expires on Nov 4, 2020. He claims he wants to sell such an option to her at a price of USD 1. The market estimates on the global index are still valid, but the discount bond price has climbed to 99 cents, and the index is quoted at 100. c) (10 pts) Should Maya buy the call option from Hedi? If she only has access to the discount bond and the index mentioned above, but she can buy and sell these assets short via the app, how can she finance this purchase without borrowing money from her family? d) (10 pts) What is the market estimate of Biden's probability of winning the elections? A couple of days later, Maya talks directly to Malik. His firm has estimated the two assets payoff matrix to be 1 2 A= 1 -1 -1 (note: there are now multiple economic scenarios relevant for the trading period) and prices now are q = (.5,1). e) (10 pts) Can you spot an arbitrage for Maya to invest in? Does the Law of One price hold on the trading platform now? Is there an s-arbitrage for s = 12 Numerically compute an arbitrage portfolio, if any exists. Explain, and show your results using a graph
