consider a one$-$period binomial model in which the underlying is at $65$ and can go up $30\%$ or down $20\%$ over next six$-$month period. The risk$-$free rate is $8\%.$ a$.$ Determine the price of a six$-$month European put option with exercise price of $70[5$ points$]$ b$.$ Assume that the put is selling $10$ in the market. Demonstrate how to execute an arbitrage transaction an calculate the rate of return. Use $100,000$ put options.