$(28$ points$)$ Consider the following information on put and call options on a stock: c$0=$$ $4\mathrm{.}50$ p$0=$$ $6\mathrm{.}80$ X $=$$ $70$ T $=139$ days S$0=$$ $67\mathrm{.}32$ r $=5\%$ Bond price$=$$ $68\mathrm{.}71$ a$.$ Use put$-$call parity to calculate the prices of the following: i$.$ Synthetic call option ii$.$ Synthetic put option iii. Synthetic bond iv$.$ Synthetic underlying Page $1$ of $9$ b$.$ For each of the synthetic instruments in part $($a$),$ identify any mispricing by comparing the actual price to the synthetic price. Instrument Actual Price Synthetic Price Mispricing Call Put Bond Stock c$.$ Based on the mispricing in part $($b$),$ illustrate an arbitrage transaction using a synthetic call. Value at expiration Transaction ST $<70$ ST $>70$ Buy actual call Synthetic call Short put Short stock Long bond Total d$.$ Based on the mispricing in part $($b$),$ illustrate an arbitrage transaction using a synthetic put. Value at expiration Transaction ST $<70$ ST $>70$ Sell actual call Buy Synthetic put Long call Long bond Short stock Total