Q&A: What should be the price of a European call...

...with an exercise price of $30 expires in 90 days, given that a European put with the same exercise price, expiration date and underlying is selling for $6. The underlying is selling for $40, and the risk free rate is 10%.

CppQuant Answer

compute the value of the synthetic call.

  • c(0) = p(0) + S(0) - X/(1 + r)^T = 6 + 40 - 30/(1 + 10%)^(90/365) = $16.7
    • time to expiration T = 90/365 = 0.2466
  • Since the synthetic call and the actual call have the same payoff, they must have the same price ($16.70) as well.

Bonus Points

  • Synthetic positions enable us to price options, because they produce the same results as options and have known prices (assuming the underlying assets make no cash payments)
  • c(0) = p(0) + S(0) - X/(1 + r)^T : the rhs is known as a synthetic call, consisting of a long put, a long position in the underlying, and a short position in the risk-free bond.
  • p(0) = c(0) + X/(1 + r)^T - S(0) : the rhs is known as a synthetic put, consisting of a long call, a short position in the underlying, and a long position in the risk-free bond.
  • p(0) + S(0) - c(0) = X/(1 + r)^T : the lhs is known as a synthetic bond.

Category: C++ Quant > Derivatives > Options

Elsewhere on BlogSpot

Tonights Lineup
KUDLOW S MONEY POLITIC$ - better benefits, required no tax increases and was risk-free... market, workers contributions were put into conservative fixed-rate guaranteed ...

June 2004
INCITE - ... all sorts of financial risk is what is known as the Risk Free Rate (RFR)... The real rate of risk is an implied figure, which is backed out from the ...

Dedicated to the Memory of Violette Szabo and...
COUNTERCOLUMN - All we have to beat is the risk-free rate of return, which is currently a fistful of unmarketable treasuries yielding perhaps 2-3...

Fed model reconsidered
INFORMATION PROCESSING - The record low yields on Treasurys sets the risk free rate (well, OK, technically TIPS are the risk free rate), and everything is measured relative to ...

Political Correctness Watch
KUDLOW S MONEY POLITIC$ - After skin cancer, there is the general risk of heat... means an exhaustive list but it clearly shows that there s no such thing as a risk-free summer...

No comments:

Post a Comment