Lesson 5 of 6 · All lessons in this module
  1. Why options need a price model: the one-period binomial setup
  2. The hedge ratio and the riskless portfolioVideo lesson
  3. From the riskless hedge to the option price
  4. Risk neutrality and risk-neutral probabilitiesVideo lesson
  5. What does and does not move a binomial option value
  6. Integrated cases: an underpriced put and a tree with a negative rate

Lesson 5 of 6 · 11 min

What does and does not move a binomial option value

In the binomial model, an option's value responds to the size of the up and down moves and to the risk-free rate, but not to the real probability of a move or to how investors feel about risk.

In short

  • A wider spread between RuR^u and RdR^d (more volatility) raises both call and put values.
  • A higher risk-free rate raises π and lowers the discount factor: the call value rises, the put value falls.
  • The actual up-probability q, the underlying's expected return and investors' risk aversion do not affect the value.
  • Two investors with opposite views on direction, but the same RuR^u, RdR^d and r, must agree on the price.
  • Binomial call and put values satisfy put-call parity: S0+p0=c0+X(1+r)−TS_0 + p_0 = c_0 + X(1+r)^{-T}.

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