Investments

What is the option worth before expiry?

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Address: Burnaby, BC, CA
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Build Black-Scholes one piece at a time, hedge with delta, find implied volatility and price payoffs by simulation. Solve has 10 questions with editable givens and worked answers.

Rates and ingredients · Step 1 of 12

Price a right that may pay nothing

Black-Scholes callCall intrinsic value

Ring: (52, 6.29)

Assumption	Meaning
European	Exercise only at expiry
No dividends	No income leaves the share before expiry
Constant inputs	Risk-free rate and volatility stay fixed
Continuous trading	Rebalance smoothly, with no trading costs
Lognormal prices	Positive share prices, smooth moves, no jumps

Rates and ingredients · Step 1 of 12

Price a right that may pay nothing

Loomfern Robotics is fictional; start with its share at $52, exercise price X = $50, expiry T = 0.75 years, yearly volatility σ = 25% and continuously compounded yearly risk-free rate r = 4%. A European call can be exercised only at expiry. The model prices both the possible upside and the wait.

Try it: Move the share price through the exercise price.

Share price today ($)$52.00

Call price

$6.29

Intrinsic

$2.00

Time value

$4.29

Intrinsic value = max((52 − 50), 0) = $2.00.

Time value = (model call − intrinsic) = (6.290243 − 2) = $4.29.

The call is in the money now; its expiry payoff is still uncertain.

Check yourself

Which contract fits this model before we add dividends?

Question 1 of 10Core

Convert the rate and discount the exercise price

Loomfern Robotics has a European option with exercise price $60.00 due in 1.5 years. The effective annual risk-free rate is 6.25%, applying to an amount lent or borrowed; there are no trading costs. (a) Convert it to a continuously compounded annual rate. (b) Find the present value of X with continuous discounting. (c) Find it again with the effective annual quote. (d) Subtract the effective-method value from the continuous-method value and explain whether changing the quote changes the cost. Carry unrounded values between steps.

Given

Option inputs

Effective annual risk-free rate6.25%

Exercise price per share$60

Time to expiry1.50 years

Solution

Continuous discountingEffective annual discounting

Ring: (1.5, 54.78)

Method	Present value
Continuous	?
Effective annual	?

Read the question and the givens first. Try the first part yourself, then press Start solving and open the working to check.

Continuous rate

Continuous PV

Effective PV

Gap; conclusion

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What is the option worth before expiry?

Price a right that may pay nothing

Price a right that may pay nothing

Convert the rate and discount the exercise price

Exam coming up and d1 and d2 are still just letters?

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