Can anyone give me a hand with the below question. How would I start it and what assumptions should I make to solve it. I would appreciate the help!
"An out-of-the-money European call option on a stock, current priced at €120, has an exercise date one year away and a strike price of €125. The option is priced at €10. The continuously compounded risk-free rate is 3% per annum.
(a) Estimate the implied volatility to within 1% per annum.
(b) Calculate the corresponding hedging portfolio in shares and cash for 1000 options on the share, quoting any results that you use.
(c) Calculate the option’s Vega.
(d) Price a put on the same stock with the same expiry date and a strike price of €115. "