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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 $93.75 and the annualized volatility of its log-returns is 57%. The option to be replicated has a strike price of $103.25 and a twelve-month maturity. The risk-free rate is currently 5.75% per year, continuously compounded. How much cash would the investor need to save or borrow to replicate the call?

A simple harmonic motion system consists of a small object attached to a light spring which oscillates with no damping on a smooth, horizontal surface. A graph of the x position of the object as a function of time is shown in the figure.  What is the amplitude of the motion?

There is a container with a rectangular window, the window dimensions are 0.101 m by 0.209 m. The container is filled with compressed gas which exerts a total force of 9.41 N perpendicular to the window surface.  Calculate the pressure (units: Pa) that the compressed gas exerts on the inside of the window.  NOTE: Watch correct use of rounding and significant figures Enter numerical answer in proper decimal format, not scientific notation Do not enter units with the answer

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 1.050-strike calls with one-year remaining maturity is 0.06 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%.

An option trader creates a delta-hedged covered call (or “buy-write”) in order to short 400 call options on a stock with a spot price of $200. The stock’s log-return has a volatility of 40 percent per year. The trader chooses to short the OOM calls with a strike price of $220 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 $20, 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 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%.