OPTIONSRachel is considering an investment in Yonan Communications, whose stock currently sells for $$65.$ A put option on Yonan$$s stock, with an exercise price of $$60,$ has a market value of $$2\mathrm{.}90.$ Meanwhile, a call option on the stock with the same exercise price and time until expiration has a market value of $$9\mathrm{.}13.$ The market believes that at the expiration of the options, the stock price will be $$55$ or $$75$ with equal probability.

What is the premium associated with the put option? The call option?

If Yonan$$s stock price increases to $$75,$ what would be the return to an investor who bought a share of the stock? If the investor bought a call option on the stock? If the investor bought a put option on the stock?

If Yonan$$s stock price decreases to $$55,$ what would be the return to an investor who bought a share of the stock? If the investor bought a call option on the stock? If the investor bought a put option on the stock?

If Rachel buys $0\mathrm{.}5$ share of Yonan Communications and sells one call option on the stock, has she created a riskless hedged investment? What is the total value of her portfolio under each scenario?

If Rachel buys $0\mathrm{.}75$ share of Yonan Communications and sells one call option on the stock, has she created a riskless hedged investment? What is the total value of her portfolio under each scenario?