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You are interested in purchasing a 1-year call for Unic Technology at a strike price of $80. The stock is currently selling for $70; a 1-year put for Unic at $80 is worth $15. The risk-free interest rate is 3%, and the yield on Unic’s 1-year senior bonds is 5%. The price of the call should be closest to:
- $5
- $6
- $7
A synthetic call can be created with a long put, long stock,
and short bond.We are given:
- P0 = $15 (put price at time 0)
- S0 = $70 (stock price at time 0)
- X = $80 (strike price)
- r = 3% (risk-free rate)
- T = 1 (1 year)
Plug this into the synthetic call formula (derived from
put-call parity):C0 = P0 + S0 – X / (1 + r)^T
= 15 + 70 – 80 / (1 + 0.03)^1
= $7.33
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