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Multistage Compound Real Options: Theory and Application

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Encyclopedia of Finance

Abstract

We explore primarily the problems encountered in multivariate normal integration and the difficulty in root-finding in the presence of unknown critical value when applying compound real call option to evaluating multistage, sequential high-tech investment decisions. We compared computing speeds and errors of three numerical integration methods. These methods, combined with appropriate root-finding method, were run by computer programs Fortran and Matlab. It is found that secant method for finding critical values combined with Lattice method and run by Fortran gave the fastest computing speed, taking only 1 s to perform the computation. Monte Carlo method had the slowest execution speed. It is also found that the value of real option is in reverse relation with interest rate and not necessarily positively correlated with volatility, a result different from that anticipated under the financial option theory. This is mainly because the underlying of real option is a nontraded asset, which brings dividend-like yield into the formula of compound real options.

In empirical study, we evaluate the initial public offering (IPO) price of a new DRAM chipmaker in Taiwan. The worldwide average sales price is the underlying variable and the average production cost of the new DRAM foundry is the exercise price. The twin security is defined to be a portfolio of DRAM manufacturing and packaging firms publicly listed in Taiwan stock markets. We estimate the dividend-like yield with two methods, and find the yield to be negative. The negative dividend-like yield results from the negative correlation between the newly constructed DRAM foundry and its twin security, implying the diversification advantage of a new generation of DRAM foundry with a relative low cost of investment opportunity. It has been found that there is only a 4.6% difference between the market IPO price and the estimated one.

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Acknowledgment

We acknowledge the financial support from National Science Council of R.O.C.

Author information

Authors and Affiliations

  1. Tamkang University, New Taipei, Taiwan, Republic of China

    William T. Lin & Chang-Wen Duan

  2. National Chiao Tung University, Hsinchu, Taiwan, Republic of China

    Cheng-Few Lee

  3. Rutgers Business School, Rutgers University, New Brunswick, USA

    Cheng-Few Lee

Authors
  1. William T. Lin
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  2. Cheng-Few Lee
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  3. Chang-Wen Duan
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Corresponding author

Correspondence to Cheng-Few Lee .

Editor information

Editors and Affiliations

  1. Dept. Finance, Rutgers University, Rockafeller Road 94, New Brunswick, 08854-8054, New Jersey, USA

    Cheng-Few Lee

  2. College of Business, San Francisco State University, Holloway Ave. 1600, San Fransisco, 94132, California, USA

    Alice C. Lee

Appendix

Appendix

The firm’s critical value \( V_i^{\rm{cr}} \) and real call options value given δ is constant and r f  = 0.08

    

\( V_2^{\rm{cr}} \)

Real call options value

Investment mode

σ v

\( V_4^{\rm{cr}} \)

\( V_3^{\rm{cr}} \)

Drezner

Lattice

MC

Drezner

Lattice

MC

Up-slo**

0.1

43.52

51.27

52.61

52.65

52.65

29.67

29.67

29.67

 

0.2

43.41

50.18

49.20

49.22

49.22

29.92

30.42

30.42

 

0.3

42.77

47.85

44.45

44.50

44.50

31.30

32.25

32.25

 

0.4

41.63

44.82

39.41

39.84

39.84

33.68

34.60

34.60

 

0.5

40.15

41.53

34.62

34.80

34.80

36.58

37.96

37.96

 

0.6

38.48

38.25

30.30

30.47

30.47

39.70

40.14

40.14

 

0.7

36.74

35.13

26.54

26.56

26.56

42.62

43.00

43.00

 

0.8

35.01

32.25

23.31

23.44

23.44

45.60

45.80

45.80

 

0.9

33.32

29.64

20.59

20.62

20.62

48.42

48.50

48.50

Down-slo**

0.1

32.92

41.60

55.77

55.79

55.79

27.78

27.77

27.77

 

0.2

31.70

40.93

55.34

55.34

55.34

27.91

27.12

27.12

 

0.3

29.76

39.14

53.60

53.72

53.72

28.90

26.87

26.87

 

0.4

27.57

36.74

50.87

51.06

51.06

30.87

28.27

28.27

 

0.5

25.36

34.13

47.67

47.84

47.84

33.41

30.58

30.58

 

0.6

23.23

31.54

44.38

44.57

44.57

36.25

33.26

33.26

 

0.7

21.26

29.08

41.21

41.47

41.47

39.04

36.00

36.00

 

0.8

19.45

26.84

38.27

38.33

38.33

41.87

38.82

38.82

 

0.9

17.82

24.81

35.61

35.72

35.72

44.59

41.50

41.50

Up, then down

0.1

32.92

47.09

55.06

55.13

55.13

28.28

28.28

28.28

 

0.2

31.70

46.82

53.78

53.85

53.85

28.43

28.36

28.36

 

0.3

29.76

45.63

51.01

51.75

51.75

29.54

29.35

29.35

 

0.4

27.57

43.69

47.39

47.53

47.53

31.63

31.54

31.54

 

0.5

25.36

41.38

43.51

43.76

43.76

34.28

34.03

34.03

 

0.6

23.23

38.95

39.70

39.83

39.83

37.20

36.80

36.80

 

0.7

21.26

36.55

36.16

36.35

36.35

40.06

39.53

39.53

 

0.8

19.45

34.27

32.95

33.06

33.06

42.95

42.28

42.28

 

0.9

17.82

32.16

30.11

30.13

30.13

45.72

44.59

44.59

Down, then up

0.1

43.52

45.37

53.90

53.90

53.90

29.17

29.18

29.18

 

0.2

43.41

42.92

52.24

52.36

52.36

29.35

29.14

29.14

 

0.3

42.77

39.47

48.94

49.06

49.06

30.56

30.00

30.00

 

0.4

41.63

35.69

44.94

44.97

44.97

32.78

31.96

31.96

 

0.5

40.15

31.99

40.83

40.90

40.90

35.56

34.49

34.49

 

0.6

38.48

28.54

36.92

37.19

37.19

38.59

37.25

37.25

 

0.7

36.74

25.44

33.38

33.58

33.58

41.41

40.06

40.06

 

0.8

35.01

22.70

30.25

30.26

30.26

44.32

42.85

42.85

 

0.9

33.32

20.31

27.51

27.83

27.83

47.08

45.88

45.88

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Lin, W.T., Lee, CF., Duan, CW. (2013). Multistage Compound Real Options: Theory and Application. In: Lee, CF., Lee, A. (eds) Encyclopedia of Finance. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5360-4_29

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  • DOI: https://doi.org/10.1007/978-1-4614-5360-4_29

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