I bought $4.5 Call (1/15/21) on 4/27 for $ .17 the day before the split. Today the value of the options is $.09. The crude oil has increased since 4/28. Would anyone help to explain on this ?
Right now, the quote for your call is $0.08 x $0.09.
What was the bid/ask spread on the day that you bought the option? If it was wide, say $0.11 x $0.17 then you are overvaluing the price change by the spread width. The bid to bid drop was only 3 cents (part of your loss was due to a wide spread). A midpoint valuation would be a drop of 5-1/2 cents. Either way, not as glaring as comparing the ask to the bid.
Right now, the quote is $0.08 x $0.09. Let's assume that it was tight at $0.16 x $0.17 when you bought the option. What would account for a loss of 8 cents on a long dated option in only 3 days? The only answer for that is a sharp contraction in implied volatility.