# Expected value vs risk-neutral pricing

John’s 70% forecast gives a $14 expected payment, discounted at the bank rate to $13.46. A half-share and a loan replicate the contract for $11.54. Discover why these answer different questions.

Use the sliders to change beliefs, strike, market quote and bank rate. Derive the 60% risk-neutral weight and compare it with the real-world forecast.

Eight paced Zon–Coach conversations explain unfamiliar notation, compare the two future states and leave time to predict and explore. Audio voices are AI-generated. The interactive and narration use the existing lesson-access system.

Canonical page: https://21ifm.com/quant/expected-value-risk-neutral

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