Q$1$a$.2$ points each; Total: $10$ Points

True or False, WHY?

$1.$ Risk neutral pricing only works when people don$$t care about risk. For this reason, risk neutral pricing only gives an

approximation of actual prices.

$2.$ A stock with a dividend yield of $2\%$ currently trade for $$100.$ The risk$-$free rate is $5\%.$ The risk neutral expected value of the

stock after one year is approximately $$107.$

$3.$ When Forward rates are higher than short maturity interest rates, it must be the case that market participants expect

interest rates to rise.

$4.$ The implied volatility is the volatility that would make the price in binomial equation agrees with the market price.

$5.$ Suppose that for a particular commodity, the $1-$month ahead forward price has on average $($historically$)$ been below the

realized future spot price. This is strong evidence that arbitrage opportunities for this commodity