No-Arbitrage Pricing in a One-Period Binomial Model

Summary

The document poses a one-period binomial market problem with a risk-free asset and a stock that can finish in either an up or down state. It asks how to establish no arbitrage, replicate a claim whose payoff is the squared terminal stock price, calculate the claim’s arbitrage-free price, and find the risk-neutral measure.

It provides the model inputs but no solution, derivation, or supporting evidence. The questions point toward checking whether state prices are positive and using replication or risk-neutral valuation, but the document does not explain those methods or give the resulting portfolio, price, or probabilities. As presented, it is a learning prompt rather than a worked example, so readers must supply the financial mathematics themselves.

Key ideas

• The prompt asks whether the specified one-period binomial market is arbitrage-free.
• It asks for a replicating portfolio for a claim based on the squared terminal stock price.
• It also asks for the claim’s no-arbitrage price and the market’s risk-neutral measure.
• No derivations or answers are included.

Tags

# One periodic binomial model


# One periodic binomial model












I need to look into a one-period Binomial model $(B_t, S_t)$ with interest rate $r = 0.1$ , $S_0 = 100$ and $$ S_t= 120 \, \text{with probability}\, 0.5 $$ $$ S_t= 60\, \text{with probability}\, 0.5 $$

a) I need to show this market has no arbitrage.

b) Find the replicating portfolio for the contingent claim $X = S^2_T$.

c) Find the price of $X$ that leads to no arbitrage.

d) Find the risk-neutral measure for this market.

Now I guess that in a) I need to show that the state-price vector is positive, but how do I do that? For the rest I have no idea and would welcome your help!

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