A client asked 3 financial institutions (A, B and C) to price a 10 year forward...

 

Transcribed Image Text:

A client asked 3 financial institutions (A, B and C) to price a 10 year forward contract to buy stock S that currently traded at $100. The company pays yearly dividend (once per year). The last dividend was paid 6 month ago at $5 per share. It is expected to pay the same amount 6 month from now as well. The risk free interest rate is 3% (continuous compounding) flat. Institution A priced the forward by assuming the stock will pay $5 dividend every 12 month starting 6 month from now; B priced it by assuming the stock pays 5% continuous dividend yield throughout the life of the forward; Trader at C believes in the next two years the company will pay $5 annual dividend but not sure if the company will adjust dividend thereafter as stock price changes. Furthermore she thinks that continuous dividend yield is not a good approximation. Hence the trader at C priced the forward with the assumption that the stock will pay $5 dividend at 6th and 18th month, and 5% proportional dividend every 12 month thereafter (i.e., at 30th month the company pays dividend equals to 5% of its then stock price. This payment will be repeated every 12 month before maturity). Assume the continuous dividend yield and the discrete annual proportional dividends are reinvested in the stock. (1) What is the forward prices institution A gave to the client? (2) What is the forward prices institution B sent to the client? (3) What is the forward prices institution C sent to the client? Explain how she calculated it. A client asked 3 financial institutions (A, B and C) to price a 10 year forward contract to buy stock S that currently traded at $100. The company pays yearly dividend (once per year). The last dividend was paid 6 month ago at $5 per share. It is expected to pay the same amount 6 month from now as well. The risk free interest rate is 3% (continuous compounding) flat. Institution A priced the forward by assuming the stock will pay $5 dividend every 12 month starting 6 month from now; B priced it by assuming the stock pays 5% continuous dividend yield throughout the life of the forward; Trader at C believes in the next two years the company will pay $5 annual dividend but not sure if the company will adjust dividend thereafter as stock price changes. Furthermore she thinks that continuous dividend yield is not a good approximation. Hence the trader at C priced the forward with the assumption that the stock will pay $5 dividend at 6th and 18th month, and 5% proportional dividend every 12 month thereafter (i.e., at 30th month the company pays dividend equals to 5% of its then stock price. This payment will be repeated every 12 month before maturity). Assume the continuous dividend yield and the discrete annual proportional dividends are reinvested in the stock. (1) What is the forward prices institution A gave to the client? (2) What is the forward prices institution B sent to the client? (3) What is the forward prices institution C sent to the client? Explain how she calculated it.

Answer rating: 100% (QA)

1 The forward price institution A gave to the client is the present value of the expected dividends ... View the full answer