Restricted Export Flexibility and Risk Management with Options and Futures



exchange rate distribution affect the firm’s optimal production and risk management
decisions. Making fairly priced currency options available to the firm has a positive effect
on production and, consequently, on expected exports and expected domestic sales if the
currency futures market is unbiased.

Appendix

A. Proof of Proposition 4

Partially differentiating the firm’s profits, Π*, as given in equation (3) with Z = 0, with
respect to S yields
11

—T = Pf Qf - H* + ∂S max(S - Pd/Pf, 0)Pf (Q* - Qd - Qf ).       (17)

∂S             ∂S

The remainder of the proof is by contradiction. Inspection of equation (17) reveals that
dn*/dS 0 if Pf (Q* Qd) H*. Given risk aversion and Pf (Q* Qd) H*, U,*)
is non-decreasing in
S for S > Pd/Pf and strictly increasing for S Pd/Pf . Hence,
Cov(U
,*),S') > 0 for Pf (Q* Qd) H*. Thus, equation (15) requires H* < Pf(Q*
Qd).

Likewise, equation (17) implies Π*∕∂S 0 if PfQf ≥ H. Thus, given PfQf ≥ H,
U,*) is non-increasing in S for S Pd/Pf and decreasing in S for S > Pd/Pf such that
the covariance in equation (15) is negative. Hence, (15) implies H
* >Pf Qf. °

B. Proof of Proposition 5

We have to show that Cov[U,(∏*), max(S Pd/Pf, 0)] is negative. Partially differentiating
Π
* with respect to S, given the optimal futures position H* as stated in Proposition 4,
results in
12

*
∂S


Pf Qf — H* < 0        for S < Pd/Pf,

Pf (Q: Qd) H* > 0 for S > Pd/Pf.

11Πφ is continuous at S = Pd/Pf but not differentiable.

12Like I li, Π* is continuous at S = Pd/Pf but not differentiable.

20



More intriguing information

1. Mortality study of 18 000 patients treated with omeprazole
2. Bridging Micro- and Macro-Analyses of the EU Sugar Program: Methods and Insights
3. Models of Cognition: Neurological possibility does not indicate neurological plausibility.
4. The Formation of Wenzhou Footwear Clusters: How Were the Entry Barriers Overcome?
5. The name is absent
6. The name is absent
7. Hemmnisse für die Vernetzungen von Wissenschaft und Wirtschaft abbauen
8. The name is absent
9. A Classical Probabilistic Computer Model of Consciousness
10. Running head: CHILDREN'S ATTRIBUTIONS OF BELIEFS
11. Are combination forecasts of S&P 500 volatility statistically superior?
12. The name is absent
13. Consciousness, cognition, and the hierarchy of context: extending the global neuronal workspace model
14. Does Market Concentration Promote or Reduce New Product Introductions? Evidence from US Food Industry
15. Towards a Strategy for Improving Agricultural Inputs Markets in Africa
16. The name is absent
17. CAPACITAÇÃO GERENCIAL DE AGRICULTORES FAMILIARES: UMA PROPOSTA METODOLÓGICA DE EXTENSÃO RURAL
18. The name is absent
19. New Evidence on the Puzzles. Results from Agnostic Identification on Monetary Policy and Exchange Rates.
20. The name is absent