Question

Please Show Your Work.

Calculate return for each of the six option contracts using (Pt – Pt-1)/P(t) where t denotes the lagged price by 1 period.

	APPL
			PrevClose	Open	Bid	Ask	Strike	Vol	Open Int	IV
1	ITM call	AAPL190118C00134000	13.70	14.90	13.65	15.10	134.00	23	69	57.15%
2	ITM call	AAPL190118C00134000	13.70	15.25	16.90	17.30	134.00	5	86	53.81%
3	ITM call	AAPL190118C00134000	15.25	15.25	20.05	20.65	134.00	5	81	72.90%
4	ITM call	AAPL190118C00134000	15.25	15.25	19.15	20.05	134.00	5	81	38.87%
5	ITM call	AAPL190118C00134000	15.25	15.25	18.15	19.05	134.00	5	81	38.87%
6	ITM call	AAPL190118C00134000	15.25	15.25	18.60	19.30	134.00	5	81	48.28%
7	ITM call	AAPL190118C00134000	15.25	15.25	19.15	19.9	134.00	5	81	60.40%
8	ITM call	AAPL190118C00134000	15.25	15.25	18.85	19.45	134.00	5	81	0.00%
9	ITM call	AAPL190118C00134000	15.25	15.25	19.9	20.05	134.00	5	81	53.32%

Answer 1

The linear or simple return between times t and t − 1 is defined as:-

Rt = Pt/P_t-1-1 − 1

The log return is defined as:-

r_t=In(P_t/P_t-1)

Note that, while P_t means “price at time t”, r_t is a shorthand for “return between time t − 1 and t” so that the notation is not really complete and its interpretation depends on the context. When needed for clarity, we shall specify returns as indexed by the start and the end point of the interval in which they are computed as, for instance, in r_t−1,t.