Put-Call Parity Basically Says That Combination of a Put, a Call

question 40

Essay

Put-call parity basically says that combination of a put, a call, and a risk-free bond must be the same value as the underlying stock. If not, at least one market is in disequilibrium. The resulting arbitrage alters the securities' prices until the value of the call plus the bond is equal to the prices of the put plus the stock. Currently, the price of a stock is $100 while the price of a call option at $100 is $10; the price of the put option is $4.59, and the rate of interest is 8 percent, so that the investor may purchase a $100 discounted note for $92.59.
a. Do these prices indicate that the financial markets are in equilibrium? Show me how you derived your answer.
b. An arbitrage opportunity should exist, but if you set up the position incorrectly, you will always sustain losses. Verify to me that if you do set up an incorrect arbitrage, you will always sustain a loss. Please use prices of the stock at $80, $100, and $120 as of the expiration date of the options.

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Definitions:

Tarsal

Relating to the bones in the foot located between the ankle and metatarsal bones, contributing to the foot's structure and movement.

Phalanges

The bones in the fingers and toes of humans and other vertebrates.

Achondroplasia

A genetic disorder affecting bone growth, leading to dwarfism characterized by short limbs, a normal-sized torso, and an enlarged head.

Epiphyses

The rounded end parts of a long bone, which grow separately from the shaft during development and later fuse to it.