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An option trader creates a delta-hedged covered call (or “buy-write”) in order to short 300 call options on a stock with a spot price of $100. The stock’s log-return has a volatility of 50 percent per year. The trader chooses to short the OOM calls with a strike price of $110 and five days until expiration (assuming 252 trading days in a year). The appropriate risk-free rate is 4 percent per year. If the price of the underlying were to immediately fall by $10, approximately what gain or loss would the trader experience? Use delta and gamma to calculate the approximation. Enter your answer as a number of dollars, rounded to the nearest $0.0001. Enter gains as positive amounts and losses as negative amounts.

An option trader has a naked option position (recall the four naked option positions are long call, long put, short call, or short put) which has the following greeks: Γ = -0.010 ρ = -1.250 |Δ| (the absolute value of delta) = 0.30 Which position do they have? Hint, short option positions flip the sign of the greeks.

An option trader has a naked option position (recall the four naked option positions are long call, long put, short call, or short put) which has the following greeks: Γ = -0.010 ρ = 1.250 |Δ| (the absolute value of delta) = 0.80 Which position do they have? Hint, short option positions flip the sign of the greeks.

An option trader has a naked option position (recall the four naked option positions are long call, long put, short call, or short put) which has the following greeks: Γ = 0.010 ρ = 1.250 |Δ| (the absolute value of delta) = 0.30 Which position do they have? Hint, short option positions flip the sign of the greeks.

Challenge You are a U.S.-based currency speculator researching call options on the EUR. The currency spot exchange rate is 1.050 USD per 1 EUR. You find that the price of 1.000-strike calls with one-year remaining maturity is 0.09 USD per EUR. If the risk-free rate in USD is currently 5.00 percent and market estimate of the exchange rate’s volatility is 15.00 percent, what EUR risk-free rate is implied by the observed call price? Enter your answer as a percentage, rounded to the nearest 0.0001%.

Suppose an investor wants to replicate a call option on the following stock and that the assumptions of the BSOPM are correct.The underlying stock’s price is $92.75 and the annualized volatility of its log-returns is 53%. The option to be replicated has a strike price of $83.50 and a twelve-month maturity. The risk-free rate is currently 5.25% per year, continuously compounded.How much cash would the investor need to save or borrow to replicate the call? (Enter a positive number for the amount saved and a negative number for the amount borrowed. Round your answer to the nearest $0.0001.

The price of ABC Co’s stock is currently $79.50 and the annualized volatility of its log-returns is 57%. The stock does not pay dividends. The risk-free rate is 4.00% per year, continuously compounded.If the price of ABC’s stock increases by $1, approximately how much will the BSOPM price of the three-month, 87.50-strike call change?  Only use delta in the approximation.

Which of the following is true about the relation between the implied volatility of option prices and the strikes of the different options? Equity index options exhibit a smirk that is higher at low strikes Currency option exhibit a smirk that is higher at low strikes Commodities exhibit a smirk that is higher at high strikes

You are an options trader who is bullish on the volatility of the underlying asset. However, you are concerned that the sensitivity of your option’s price to the volatility of the underlying will decay quickly. Therefore, you decide to calculate a new option greek, which you name “veta,” which measures how the sensitivity changes over time. How would you find a formula for veta?

An option trader creates a delta-hedged covered call (or “buy-write”) in order to short 300 call options on a stock with a spot price of $100. The stock’s log-return has a volatility of 60 percent per year. The trader chooses to short the OOM calls with a strike price of $130 and five days until expiration (assuming 252 trading days in a year). The appropriate risk-free rate is 4 percent per year. If the price of the underlying were to immediately fall by $10, approximately what gain or loss would the trader experience? Use delta and gamma to calculate the approximation. Enter your answer as a number of dollars, rounded to the nearest $0.0001. Enter gains as positive amounts and losses as negative amounts.