If underlying is non-dividend paying, then the time value of an American call option is positive, hence American call should never be exercised early. True False
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- If the time to expiration falls and the put price rises, then what has happened to the put option’s implied volatility?My question is for a synthetic call option why do we need to borrow the present value of the strike price and what does it mean in a simple language explanation. Similarly why do we need to lend the present value of the stock at risk-free rate and what does it mean in simple language explanation? Please also clarify the significance of risk free rate? Why is it used in put call parity. Synthetic Call Option: If an investor believes that a call option is over-priced, then he/she can sell the call on the market and replicate a synthetic call. Borrow the present value of the strike price at the risk free rate and purchase the underlying stock and a put. Synthetic Put Option: Similar to the synthetic call option. A synthetic put can be created by re-arranging the put-call parity relationship, if the trader believes the put is overvalued. Synthetic Stock: A synthetic stock can also be created by rearranging the put-call parity identity. In this case, the investor will buy the…Suppose that C is the price of a European call option to purchase a security whose present price is S. Show that if C>S then there is an opportunity for arbitrage (ie. riskless profit). Assume the interest rate r=0 so present value calculations are unnecessary.
- Suppose that C is the price of a European call option to purchase a security whose present price is S.Show that if C > S then there is an opportunity for arbitrage (i.e. riskless profit). You may assume theinterest rate is r = 0 so that present value calculations are unnecessary.Which of the following inputs is not required to price option using the Black‐Scholes model? a) the asset price b) the time to maturity c) the asset’s risk premium d) the risk‐free rate of interestAn up-and-out barrier call option with barrier B, strike price K and exercise time T has payoff H(T) = (S(T) − K) + if max {S(t)| 0 ≤ t ≤ T} < B, 0 otherwise, that is, the payoff is that of a call option if the underlying stock price does not reach or exceed the barrier B at any time up to and including time T, and 0 otherwise. For an up-and-out barrier call option with barrier B = 140, strike price K = 90 and exercise time T = 3 in the binomial model with parameters U = 0.2, D = −0.1, R = 0.1 and S(0) = 100 compute the following. (a) The option price at time 0;
- Suppose stocks X and Y have equal current prices but different volatilities of returns, ax < øy; what would be more expensive: a call option on X or Y? Please discuss.Suppose that C is the price of a European call option to purchase a security whose present price is S. Show that if C>S then there is an opportunity for arbitrage (i.e. risk-less profit). You may assume the interest rate is r=0 so that the present value calculations are unnecessary.All else equal, will a call option with a high exercise price have a higher or lower hedge ratio than one with a low exercise price?
- 2. In the context of binomial option pricing model, a decrease in the stock price volatility will reduce the current option value True or falseTick all those statements on options that are correct (and don't tick those statements that are incorrect). a. The put-call parity formula necessarily requires the assumption that the share price follows a geometric Brownain motion. b. In general the equation S(T) + (K − S(T))† = (S(T) – K)+ + K is valid. An American put option should never be exercised before the expiry time. C. d. The Black-Scholes formula is based on the assumption that the share price follows a geometric Brownian motion. e. If interest is compounded continuously then the put-call parity formula is P + S(0) = C + Ke¯T where T is the expiry time.IT IS NOT DELTA Option _______ is a percentage change in the value of the option per 1% change in the value of the underlying security. b. Rho c. Elasticity d. Theta