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Table 1 Option values across the level of ambiguity

From: Effects of ambiguity on innovation strategies

 

High level of ambiguity

Modest level of ambiguity

Low level of ambiguity

\({\mathbb{E}}(T)\)

\({X}_{h}\)

\({X}_{l}\)

Option value

\({X}_{h}\)

\({X}_{l}\)

Option value

\({X}_{h}\)

\({X}_{l}\)

Option value

0.0

1.000

0.967

1.157

1.000

0.961

1.157

1.000

0.956

1.157

0.5

1.010

0.939

1.123

1.015

0.927

1.120

1.020

0.917

1.119

1.0

1.019

0.948

1.090

1.029

0.941

1.086

1.040

0.935

1.083

1.5

1.029

0.958

1.058

1.044

0.954

1.052

1.060

0.953

1.048

2.0

1.039

0.967

1.028

1.060

0.968

1.020

1.081

0.972

1.016

2.5

1.049

0.976

0.999

1.075

0.982

0.990

1.102

0.991

0.986

3.0

1.059

0.985

0.972

1.091

0.997

0.963

1.123

1.000

0.959

3.5

1.070

0.995

0.946

1.107

1.000

0.938

1.145

1.000

0.933

4.0

1.080

1.000

0.922

1.123

1.000

0.914

1.168

1.000

0.908

4.5

1.090

1.000

0.900

1.139

1.000

0.890

1.191

1.000

0.884

5.0

1.101

1.000

0.878

1.156

1.000

0.867

1.214

1.000

0.861

  1. \({X}_{h}\) represents the threshold at which a future innovation arrives and this value corresponds to the expected time of its arrival. \({X}_{l}\) represents the optimal threshold at which managers invest optimally in the current innovation. “Option value” is the sum of the values of the options, \(F\) and \(G\), given the values of \({X}_{h}\) and \({X}_{l}\). “High,” “Modest,” and “Low” levels of ambiguity correspond to \(c=0.2\), \(0.3\), and \(0.4\), respectively