The Future Does Not Belong to China: The End of Its Economic Boom

China’s meteoric rise to the world’s second-largest economy over the last four decades is slowing. Key factors signal the end of its economic boom: 1. Demographic Crisis: Rapid aging, declining birth rates, and a shrinking workforce are raising labor costs, straining public resources, and reducing domestic consumption. 2. Loss of Competitive Edge: Countries like India and Vietnam are attracting manufacturing as China faces higher wages and automation pressures. 3. Government Policies: Crackdowns on the private sector, real estate instability, and increasing state control have stifled investment and innovation. 4. Geopolitical Tensions: Trade wars, sanctions, and global distrust have weakened China’s economic influence. Structural challenges, including a real estate crisis and slowing productivity, further jeopardize growth. While China will remain a global economic force, its ambitions to surpass the U.S. now seem unrealistic. The future belongs to adaptable economies, and China faces significant hurdles ahead.

The Elasticity and Risk Premium of an Option Portfolio

The elasticity of a portfolio of call options can be expressed as

Ω_portfolio = _i=1ⁿΣω_iΩ _i where Ω _i is the elasticity of the ith call option and ω_i is the percentage of the portfolio comprised of the ith call option.

The risk premium on the portfolio - where all call options are based on the same underlying asset - is

γ - r = Ω_portfolio(α - r)

Meaning of variables:

γ = expected annual continuously compounded return on the option.

α = expected annual continuously compounded return on the underlying asset (most often a stock).

Ω = option elasticity.

r = annual continuously compounded risk-free interest rate.

Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 12,

p. 395 

The delta-gamma approximation and A delta-hedged

A market-maker sells assets or contracts to buyers and buys them from sellers. He is an intermediary between the buyers and sellers. A market-maker's function is in contrast toproprietary trading, which is "trading to express an investment strategy" (McDonald, p. 414).

A delta-hedged position is a position designed to earn the risk-free rate of interest and is used to offset the risk of an option position.

The delta-gamma approximation is used to estimate option price movements if the underlying stock price changes.

The delta-gamma approximation for call options can be expressed via the following formula:

C(S_t+h) = C(S_t) + є∆(S_t) + (1/2)є²Γ(S_t)

For a put option, the same formula holds, but delta is now negative - so the put price will decrease if the stock price increases.

Meaning of variables:

S_t = stock price at time t.

S_t+h = stock price at time t+h.

C = call option price.

є = stock price change from time t to time t + h.

∆ = option delta.

Γ = option gamma.

Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 13, pp. 413-425.

Put-call parity for European options

Put-call parity for European options with the same strike price and time to expiration is

Call - put = present value of (forward price - strike price)

Equation for put-call parity:
C(K, T) - P(K, T) = PV_0,T(F_0,T - K) = e^-rT(F_0,T - K)

Meaning of variables:

K = strike price of the options

T = time to expiration of the options

C(K, T) = price of a European call with strike price K and time to expiration T.

P(K, T) = price of a European put with strike price K and time to expiration T.

F_0,T = forward price for the underlying asset.

PV_0,T = the present value over the life of the options.

e^-rT*F_0,T = prepaid forward price for the asset.

e^-rT*K= prepaid forward price for the strike.

r = the continuously compounded interest rate.

Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 9, p. 282.

MFE question from SOA's Sample question

 Company A is a U.S. international company, and Company B is a Japanese local
company.  Company A is negotiating with Company B to sell its operation in
Tokyo to Company B.  The deal will be settled in Japanese yen.  To avoid a loss at
the time when the deal is closed due to a sudden devaluation of yen relative to
dollar, Company A has decided to buy at-the-money dollar-denominated yen put of
the European type to hedge this risk.
 You are given the following information:
(i) The deal will be closed 3 months from now.
(ii) The sale price of the Tokyo operation has been settled at 120 billion Japanese
yen.
(iii) The continuously compounded risk-free interest rate in the U.S. is 3.5%.
(iv) The continuously compounded risk-free interest rate in Japan is 1.5%.
(v) The current exchange rate is 1 U.S. dollar = 120 Japanese yen.
(vi) The natural logarithm of the yen per dollar exchange rate is an arithmetic
Brownian motion with daily volatility 0.261712%.
(vii)  1 year = 365 days; 3 months = ¼ year.
 Calculate Company A’s option cost.