Blog

A horizontal pipe of 35 cm2 cross-sectional area carries water at a speed of 2.5 m/s. This pipe flows into a smaller pipe with a 18 cm2 cross-sectional area. Calculate the speed (units: m/s) of water flow in the smaller pipe. 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

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.