Assume the risk-free rate of interest is 2% per annum continuously compounded (or any risk-free rate from the market with a brief introduction. If your warrants data are collected from 01 March 2021 until 31 March 2021, then the latest date of your data is defined as 31 March 2021.

- Discuss the moneyness of your call and put warrants based on the latest date of your data.
- If your call and put warrants are now expired at the latest date of your data. In this example, the expiration date was 31 March 2021. Determine the fair value of the call and put warrants.
- Discuss at least 2 trading strategies that involve underlying, call, and put warrants.
- Based on your data. Calculate
**a)**The daily log return of the underlying asset, i.e

where R𝑡 is the log return at time T₁, and S𝑡 is the underlying price at time T𝑡.**b)**Expected annualized return and annualized volatility of the underlying asset.**c)**Time to maturity of both call and put options, assuming that the current date is the latest date of your data. In this example, the current date is 31 March 2021. - Now change the current date to a new date (but early than 31 March 2021) such that your time to maturity is an integer multiplied by 7 (1 week). For example, let’s say an option expired on 29 May 2021. The time to maturity was 59 days if it is based on 31 March 2021, but it is not an integer multiplied by 7. The smallest integer number multiple of 7 after 59 days is 63 days. Hence, your NEW current date is 27 March 2021. Let ℎ = 7/365, (1 week), based on the input in (4) and the new current date, determine (for all call and put warrants)
**(a)**the number of periods for the binomial tree;**(b)**the up and down factors, 𝑢𝑢 and 𝑑𝑑, respectively;**(c)**the risk-neutral probabilities;**(d)**the real probabilities;**(e)**the current price of the warrant based on your binomial tree in 5(a);**(f)**the true discount rate of the option at the current date;**(g)**explain why the observed current option price is different from 5(e). - Determine the theoretical price of the warrants under the Black-Scholes framework.

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