Boa

Q1: What does the payoff look like in a vanilla European call chart? I started to panic here. The payoff and profit were a bit mixed up, and I wasn't reminded that S<K was above 0. Q2: Continuing with the European call chart: They asked me to draw the value option and payoff on a single chart. A: No problem. I used the Black-Scholes formula and drew a roughly exponential one. Q3: Focusing on details, what happens in the lower left corner of this chart (when both the value option and S are close to 0) – deep out of the money? A: I think I answered incorrectly here. I hope someone can correct me. I said the value of the option is non-negative (I gave a rough explanation, saying that otherwise you could directly buy the underlying). Then the interviewer asked, substituting into Black-Scholes, if S=0 or approach 0, then term 1 disappears, leaving the strike-dominated term which is non-negative (due to the exponent). Would this result in a negative option value? I think what he said makes sense, but I don't quite understand how this works in reality. Q4. Assuming a six-month European call option trike of 100, what is today's value? A: I was completely stumped. My first instinct was to calculate it directly using Black-Scholes, so I explained my assumptions. Six months is half a year, so I set T to 1/2, and the interest rate was assumed to be 2%. I didn't consider the volume and said $2. Realizing later that I was terribly wrong, I just checked on ChatGPT and it says around 6.1. (How do I mentally calculate this?!)